# Publications

2022
Mourtas, S. D., & Katsikis, V. N. (2022). Exploiting the Black-Litterman framework through error-correction neural networks. Neurocomputing, 498, 43-58. WebsiteAbstract
The Black-Litterman (BL) model is a particularly essential analytical tool for effective portfolio management in financial services sector since it enables investment analysts to integrate investor views into market equilibrium returns. In this research, we define and study the continuous-time BL portfolio optimization (CTBLPO) problem as a time-varying quadratic programming (TVQP) problem. The investor’s views in the CTBLPO problem are regarded as a forecasting problem, and they are generated by a novel neural network (NN) model. More precisely, employing a novel multi-function activated by a weights-and-structure-determination for time-series (MAWTS) algorithm, a 3-layer feed-forward NN model, called MAWTSNN, is proposed for handling time-series modeling and forecasting problems. Then, using real-world datasets, the CTBLPO problem is approached by two different TVQP NN solvers. These solvers are the zeroing NN (ZNN) and the linear-variational-inequality primal–dual NN (LVI-PDNN). The experiment findings illustrate and compare the performances of the ZNN and LVI-PDNN in three various portfolio configurations, as well as indicating that the MAWTSNN is an excellent alternative to the traditional approaches. To promote and contend the outcomes of this research, we created two MATLAB repositories for the interested user, that are publicly accessible on GitHub.
Stanujkic, D., Karabasevic, D., Popovic, G., Smarandache, F., Stanimirović, P. S., Saračević, M., & Katsikis, V. N. (2022). A Single Valued Neutrosophic Extension of the Simple WISP Method. Informatica, 1–17. Vilnius University Institute of Data Science and Digital Technologies.
Mosić, D., Stanimirović, P. S., & Katsikis, V. N. (2022). Properties of the CMP inverse and its computation. Computational and Applied Mathematics, 41(4), 131. presented at the 2022. Publisher's VersionAbstract
This manuscript aims to establish various representations for the CMP inverse. Some expressions for the CMP inverse of appropriate upper block triangular matrix are developed. Successive matrix squaring algorithm and the method based on the Gauss–Jordan elimination are considered for calculating the CMP inverse. As an application, the solvability of several restricted systems of linear equations (RSoLE) is investigated in terms of the CMP inverse. Illustrative examples and examples on randomly generated large-scale matrices are presented.
Simos, T. E., Katsikis, V. N., Mourtas, S. D., Stanimirović, P. S., & Gerontitis, D. (2022). A higher-order zeroing neural network for pseudoinversion of an arbitrary time-varying matrix with applications to mobile object localization. Information Sciences, 600, 226-238. WebsiteAbstract
The hyperpower family of iterative methods with arbitrary convergence order is one of the most used methods for estimating matrix inverses and generalized inverses, whereas the zeroing neural network (ZNN) is a type of neural dynamics developed to solve time-varying problems in science and engineering. Since the discretization of ZNN dynamics leads to the Newton iterative method for solving the matrix inversion and generalized inversion, this study proposes and investigates a family of ZNN dynamical models known as higher-order ZNN (HOZNN) models, which are defined on the basis of correlation with hyperpower iterations of arbitrary order. Because the HOZNN dynamical system requires error function powers, it is only applicable to square error functions. In this paper, we extend the original HOZNN dynamic flows to arbitrary time-dependent real matrices, both square and rectangular, and sign-bi-power activation is used to investigate the finite-time convergence of arbitrary order HOZNN dynamics. The proposed models are theoretically and numerically tested under three activation functions, and an application in solving the angle-of-arrival (AoA) localization problem demonstrates the effectiveness of the proposed design.
Kornilova, M., Kovalnogov, V., Fedorov, R., Zamaleev, M., Katsikis, V. N., Mourtas, S. D., & Simos, T. E. (2022). Zeroing Neural Network for Pseudoinversion of an Arbitrary Time-Varying Matrix Based on Singular Value Decomposition. Mathematics, 10. WebsiteAbstract
Many researchers have investigated the time-varying (TV) matrix pseudoinverse problem in recent years, for its importance in addressing TV problems in science and engineering. In this paper, the problem of calculating the inverse or pseudoinverse of an arbitrary TV real matrix is considered and addressed using the singular value decomposition (SVD) and the zeroing neural network (ZNN) approaches. Since SVD is frequently used to compute the inverse or pseudoinverse of a matrix, this research proposes a new ZNN model based on the SVD method as well as the technique of Tikhonov regularization, for solving the problem in continuous time. Numerical experiments, involving the pseudoinversion of square, rectangular, singular, and nonsingular input matrices, indicate that the proposed models are effective for solving the problem of the inversion or pseudoinversion of time varying matrices.
Khan, A. T., Cao, X., Brajevic, I., Stanimirovic, P. S., Katsikis, V. N., & Li, S. (2022). Non-linear Activated Beetle Antennae Search: A novel technique for non-convex tax-aware portfolio optimization problem. Expert Systems with Applications, 116631. WebsiteAbstract
The non-convex tax-aware portfolio optimization problem is traditionally approximated as a convex problem, which compromises the quality of the solution and converges to a local-minima instead of global minima. In this paper, we proposed a non-deterministic meta-heuristic algorithm called Non-linear Activated Beetle Antennae Search (NABAS). NABAS explores the search space at the given gradient estimate measure until it is smaller than a threshold known as “Activation Threshold”, which increases its convergence rate and avoids local minima. To test the validity of NABAS, we formulated an optimization-based tax-aware portfolio problem. The objective is to maximize the profit and minimize the risk and tax liabilities and fulfill other constraints. We collected stock data of 20 companies from the NASDAQ stock market and performed a simulation using MATLAB. A comprehensive comparison is made with BAS, PSO, and GA algorithms. The results also showed that a better-optimized portfolio is achieved with a non-convex problem than a convex problem.
Mourtas, S. D., Katsikis, V. N., & Kasimis, C. (2022). Feedback Control Systems Stabilization Using a Bio-inspired Neural Network. EAI Endorsed Transactions on AI and Robotics, 1, 1–13. presented at the Feb. Publisher's Version
Khan, A. T., Cao, X., Li, S., Katsikis, V. N., Brajevic, I., & Stanimirovic, P. S. (2022). Fraud detection in publicly traded U.S firms using Beetle Antennae Search: A machine learning approach. Expert Systems with Applications, 191, 116148. WebsiteAbstract
In this paper, we present a fraud detection framework for publicly traded firms using an optimization approach integrated with a meta-heuristic algorithm known as Beetle Antennae Search (BAS). Existing techniques include human resources, like financial experts and audit teams, to determine the ambiguities or financial frauds in the companies based on financial and non-financial ratios. It is a laborious task, time-consuming, and prone to errors. We designed an optimization problem to minimize the loss function based on a non-linear decision function combined with the maximization of recall (Sensitivity and Specificity). We solved the optimization problem iteratively using the BAS. It is a nature-inspired algorithm and mimics the beetle’s food-searching nature. It includes a single searching particle to find an optimal solution to the optimization problem in n-dimensional space. We used a benchmark dataset collected from SEC’s Accounting and Auditing Enforcement Releases (AAERs) for the simulation. It includes 28 raw financial variables and the data collected between 1991–2008. For the comparison, we evaluated the performance of BAS with the recently proposed approach using RUSBoost. We also compared it with some additional algorithms, i.e., Logit and SVM-FK. The results showed that BAS is comparable with these algorithms and outperformed them in time consumption.
Katsikis, V. N., Stanimirovic, P. S., Mourtas, S. D., Li, S., & Cao, X. (2022). Towards Higher Order Dynamical Systems (Book Chapter). In I. Kyrchei (Ed.), Generalized Inverses - Algorithms and Applications (1st ed., pp. 207-239). Nova Science Publications. Website
Katsikis, V. N., Mourtas, S. D., Stanimirović, P. S., Li, S., & Cao, X. (2022). Time-varying mean–variance portfolio selection problem solving via LVI-PDNN. Computers and Operations Research, 138, 105582. presented at the 2022. Publisher's VersionAbstract
It is widely acclaimed that the Markowitz mean–variance portfolio selection is a very important investment strategy. One approach to solving the static mean–variance portfolio selection (MVPS) problem is based on the usage of quadratic programming (QP) methods. In this article, we define and study the time-varying mean–variance portfolio selection (TV-MVPS) problem both in the cases of a fixed target portfolio’s expected return and for all possible portfolio’s expected returns as a time-varying quadratic programming (TVQP) problem. The TV-MVPS also comprises the properties of a moving average. These properties make the TV-MVPS an even greater analysis tool suitable to evaluate investments and identify trading opportunities across a continuous-time period. Using an originally developed linear-variational-inequality primal–dual neural network (LVI-PDNN), we also provide an online solution to the static QP problem. To the best of our knowledge, this is an innovative approach that incorporates robust neural network techniques to provide an online, thus more realistic, solution to the TV-MVPS problem. In this way, we present an online solution to a time-varying financial problem while eliminating static method limitations. It has been shown that when applied simultaneously to TVQP problems subject to equality, inequality and boundary constraints, the LVI-PDNN approaches the theoretical solution. Our approach is also verified by numerical experiments and computer simulations as an excellent alternative to conventional MATLAB methods.
2021
Stanujkić, D., Karabašević, D., Popović, G., Zavadskas, E. K., Saračević, M., Stanimirović, P. S., Katsikis, V. N., et al. (2021). Comparative Analysis of the Simple WISP and Some Prominent MCDM Methods: A Python Approach. Axioms, 10. Publisher's VersionAbstract
This article presents a comparison of the results obtained using the newly proposed Simple Weighted Sum Product method and some prominent multiple criteria decision-making methods. For comparison, several analyses were performed using the Python programming language and its NumPy library. The comparison was also made on a real decision-making problem taken from the literature. The obtained results confirm the high correlation of the results obtained using the Simple Weighted Sum Product method and selected multiple criteria decision-making methods such as TOPSIS, SAW, ARAS, WASPAS, and CoCoSo, which confirms the usability of the Simple Weighted Sum Product method for solving multiple criteria decision-making problems.
Simos, T. E., Katsikis, V. N., & Mourtas, S. D. (2021). Multi-input bio-inspired weights and structure determination neuronet with applications in European Central Bank publications. Mathematics and Computers in Simulation. presented at the 2021. Publisher's VersionAbstract
This paper introduces a 3-layer feed-forward neuronet model, trained by novel beetle antennae search weights-and-structure-determination (BASWASD) algorithm. On the one hand, the beetle antennae search (BAS) algorithm is a memetic meta-heuristic optimization algorithm capable of solving combinatorial optimization problems. On the other hand, neuronets trained by a weights-and-structure-determination (WASD) algorithm are known to resolve the shortcomings of traditional back-propagation neuronets, including slow speed of training and local minimum. Combining the BAS and WASD algorithms, a novel BASWASD algorithm is created for training neuronets, and a multi-input BASWASD neuronet (MI-BASWASDN) model is introduced. Using a power sigmoid activation function and while managing the model fitting and validation, the BASWASD algorithm finds the optimal weights and structure of the MI-BASWASDN. Four financial datasets, taken from the European Central Bank publications, validate and demonstrate the MI-BASWASDN model’s outstanding learning and predicting performance. Also included is a comparison of the MI-BASWASDN model to three other well-performing neural network models, as well as a MATLAB kit that is publicly available on GitHub to promote and support this research.
Katsikis, V. N., Stanimirovic, P. S., Mourtas, S. D., Xiao, L., Karabasevic, D., & Stanujkic, D. (2021). Zeroing Neural Network with Fuzzy Parameter for Computing Pseudoinverse of Arbitrary Matrix. IEEE Transactions on Fuzzy Systems. Publisher's Version
Simos, T. E., Katsikis, V. N., & Mourtas, S. D. (2021). A fuzzy WASD neuronet with application in breast cancer prediction. Neural Computing and Applications. presented at the 2021. Publisher's VersionAbstract
Cancer is one of the world’s leading causes of human mortality, and the most prevalent type is breast cancer. However, when diagnosed early, breast cancer may be treated. In this paper, a 5-layer feed-forward neuronet model, trained by a novel fuzzy WASD (weights-and-structure-determination) algorithm, called FUZWASD, is introduced and employed to predict whether the breast cancer is benign or malignant. In general, WASD-trained neuronets are known to overcome the limitations of traditional back-propagation neuronets, including slow training speed and local minimum; however, multi-input WASD-trained neuronets with no dimension explosion weakness are few. In this work, a novel FUZWASD algorithm for training neuronets is modeled by embedding a fuzzy logic controller (FLC) in a WASD algorithm, and a multi-input FUZWASD neuronet (MI-FUZWASDN) model for classification problems with no dimension explosion weakness is proposed. The FUZWASD algorithm uses a FLC to map the input data into a specific interval that enhances the accuracy of the weights-direct-determination (WDD) method. In this way, the FUZWASD algorithm detects the optimal weights and structure of the MI-FUZWASDN using a power softplus activation function and while handling the model fitting and validation. Applications on two diagnostic breast cancer datasets validate and demonstrate the MI-FUZWASDN model’s exceptional learning and predicting performance. In addition, for the intrigued user, we have created a MATLAB kit, which is freely accessible via GitHub, to promote and support the results of this work.
Mourtas, S. D., & Katsikis, V. N. (2021). V-Shaped BAS: Applications on Large Portfolios Selection Problem. Computational Economics. presented at the 2021. Publisher's VersionAbstract
The beetle antennae search (BAS) algorithm is a memetic meta-heuristic optimization algorithm capable of solving combinatorial optimization problems. In this paper, the binary version of BAS (BBAS) is modified by adding a V-shaped transfer function. In this way, we introduce the V-shaped transfer function-based binary BAS (VSBAS) algorithm, which is a more effective and efficient version of BBAS in the case of large input data. Applications using real-world data sets on a binary Markowitz-based portfolio selection (BMPS) problem validate the excellent performance of VSBAS on large input data and demonstrate that it is a marvelous alternative against other ordinary memetic meta-heuristic optimization algorithms. Note that, because the meta-heuristic algorithms compared in this paper are directly applicable only to unconstrained optimization, the penalty function method was used to keep their solutions in the feasible district. In order to support and promote the findings of this work, we have constructed a complete MATLAB package for the interested user, which is freely available through GitHub.
Simos, T. E., Mourtas, S. D., & Katsikis, V. N. (2021). Time-varying Black–Litterman portfolio optimization using a bio-inspired approach and neuronets. Applied Soft Computing, 112, 107767. WebsiteAbstract
The Black–Litterman model is a very important analytical tool for active portfolio management because it allows investment analysts to incorporate investor’s views into market equilibrium returns. In this paper, we define and study the time-varying Black–Litterman portfolio optimization under nonlinear constraints (TV-BLPONC) problem as a nonlinear programming (NLP) problem. More precisely, the nonlinear constraints refer to transaction costs and cardinality constraints. Furthermore, a speedy weights-and-structure-determination (WASD) algorithm for the power-activation feed-forward neuronet (PFN) is presented to solve time-series modeling and forecasting problems. Inhere, the investor’s views in the TV-BLPONC problem are considered as a forecasting problem and, thus, they are produced by the WASD-based PFN. In addition, using the beetle antennae search (BAS) algorithm a computational method is introduced to solve the TV-BLPONC problem. For all we know, this is an innovative approach that integrates modern neural network and meta-heuristic optimization methods to provide a solution to the TV-BLPONC problem in large portfolios. Our approach is tested on portfolios of up to 90 stocks with real-world data, and the results show that it is more than 30 times faster than other methods. Our technique’s speed and precision are verified in this way, showing that it is an outstanding alternative to ordinary methods. In order to support and promote the findings of this work, we have constructed two complete MATLAB packages for the interested user, which are freely available through GitHub.
Mosić, D., Stanimirović, P. S., & Katsikis, V. N. (2021). Weighted composite outer inverses. Applied Mathematics and Computation, 411, 126493. WebsiteAbstract
In order to extend and unify the definitions of W-weighted DMP, W-weighted MPD, W-weighted CMP and composite outer inverses, we present the weighted composite outer inverses. Precisely, the notions of MNOMP, MPMNO and MPMNOMP inverses are introduced as appropriate expressions involving the (M,N)-weighted (B,C)-inverse and Moore–Penrose inverse. Basic properties and a number of characterizations for the MNOMP, MPMNO or MPMNOMP inverse are discovered. Various representations and characterizations of weighted composite outer inverses are studied. General solutions for certain systems of linear equations are given in terms of weighted composite outer inverses. Numerical examples are presented on randomly generated matrices of various orders.
Stanujkić, D., Karabašević, D., Popović, G., Stanimirović, P. S., Saračević, M., Smarandache, F., Katsikis, V. N., et al. (2021). A New Grey Approach for Using SWARA and PIPRECIA Methods in a Group Decision-Making Environment. Mathematics, 9. Publisher's VersionAbstract
The environment in which the decision-making process takes place is often characterized by uncertainty and vagueness and, because of that, sometimes it is very hard to express the criteria weights with crisp numbers. Therefore, the application of the Grey System Theory, i.e., grey numbers, in this case, is very convenient when it comes to determination of the criteria weights with partially known information. Besides, the criteria weights have a significant role in the multiple criteria decision-making process. Many ordinary multiple criteria decision-making methods are adapted for using grey numbers, and this is the case in this article as well. A new grey extension of the certain multiple criteria decision-making methods for the determination of the criteria weights is proposed. Therefore, the article aims to propose a new extension of the Step-wise Weight Assessment Ratio Analysis (SWARA) and PIvot Pairwise Relative Criteria Importance Assessment (PIPRECIA) methods adapted for group decision-making. In the proposed approach, attitudes of decision-makers are transformed into grey group attitudes, which allows taking advantage of the benefit that grey numbers provide over crisp numbers. The main advantage of the proposed approach in relation to the use of crisp numbers is the ability to conduct different analyses, i.e., considering different scenarios, such as pessimistic, optimistic, and so on. By varying the value of the whitening coefficient, different weights of the criteria can be obtained, and it should be emphasized that this approach gives the same weights as in the case of crisp numbers when the whitening coefficient has a value of 0.5. In addition, in this approach, the grey number was formed based on the median value of collected responses because it better maintains the deviation from the normal distribution of the collected responses. The application of the proposed approach was considered through two numerical illustrations, based on which appropriate conclusions were drawn.
Katsikis, V. N., Mourtas, S. D., Stanimirović, P. S., & Zhang, Y. (2021). Continuous-Time Varying Complex QR Decomposition via Zeroing Neural Dynamics. Neural Processing Letters. presented at the 2021. Publisher's VersionAbstract
QR decomposition (QRD) is of fundamental importance for matrix factorization in both real and complex cases. In this paper, by using zeroing neural dynamics method, a continuous-time model is proposed for solving the time-varying problem of QRD in real-time. The proposed dynamics use time derivative information from a known real or complex matrix. Furthermore, its theoretical analysis is provided to substantiate the convergence and effectiveness of solving the time-varying QRD problem. In addition, numerical experiments in four different-dimensional time-varying matrices show that the proposed model is effective for solving the time-varying QRD problem both in the case of a real or a complex matrix as input.
Stanujkić, D., Karabašević, D., Popović, G., Stanimirović, P. S., Smarandache, F., Saračević, M., Katsikis, V. N., et al. (2021). An Innovative Grey Approach for Group Multi-Criteria Decision Analysis Based on the Median of Ratings by Using Python. Axioms, 10. Publisher's VersionAbstract
Some decision-making problems, i.e., multi-criteria decision analysis (MCDA) problems, require taking into account the attitudes of a large number of decision-makers and/or respondents. Therefore, an approach to the transformation of crisp ratings, collected from respondents, in grey interval numbers form based on the median of collected scores, i.e., ratings, is considered in this article. In this way, the simplicity of collecting respondents’ attitudes using crisp values, i.e., by applying some form of Likert scale, is combined with the advantages that can be achieved by using grey interval numbers. In this way, a grey extension of MCDA methods is obtained. The application of the proposed approach was considered in the example of evaluating the websites of tourism organizations by using several MCDA methods. Additionally, an analysis of the application of the proposed approach in the case of a large number of respondents, done in Python, is presented. The advantages of the proposed method, as well as its possible limitations, are summarized.
Katsikis, V. N., & Mourtas, S. D. (2021). Binary Beetle Antennae Search Algorithm for Tangency Portfolio Diversification. Journal of Modeling and Optimization, 13(1). Publisher's VersionAbstract
The tangency portfolio, also known as the market portfolio, is the most efficient portfolio and arises from the intercept point of the Capital Market Line (CML) and the efficient frontier. In this paper, a binary optimal tangency portfolio under cardinality constraint (BOTPCC) problem is defined and studied as a nonlinear programming (NLP) problem. Because such NLP problems are widely approached by heuristic, a binary beetle antennae search algorithm is employed to provide a solution to the BTPSCC problem. Our method proved to be a magnificent substitute to other evolutionary algorithms in real-world datasets, based on numerical applications and computer simulations.
Katsikis, V. N., & Mourtas, S. D. (2021). Portfolio Insurance and Intelligent Algorithms. In S. Patnaik, Tajeddini, K., & Jain, V. (Eds.), Computational Management: Applications of Computational Intelligence in Business Management (pp. 305 - 323). presented at the 2021, Cham: Springer International Publishing. Publisher's VersionAbstract
Minimizing portfolio insurance (PI) costs is an investment strategy of great importance. In this chapter, by converting the classical minimum-cost PI (MCPI) problem to a multi-period MCPI (MPMCPI) problem, we define and investigate the MPMCPI under transaction costs (MPMCPITC) problem as a nonlinear programming (NLP) problem. The problem of MCPI gets more genuine in this way. Given the fact that such NLP problems are widely handled by intelligent algorithms, we are introducing a well-tuned approach that can solve the challenging MPMCPITC problem. In our portfolios’ applications, we use real-world data and, along with some of the best memetic meta-heuristic and commercial methods, we provide a solution to the MPMCPITC problem, and we compare their solutions to each other.
Stanimirović, P. S., Katsikis, V. N., Jin, L., & Mosić, D. (2021). Properties and computation of continuous-time solutions to linear systems. Applied Mathematics and Computation, 405. presented at the 2021. Publisher's VersionAbstract
We investigate solutions to the system of linear equations (SoLE) in both the time-varying and time-invariant cases, using both gradient neural network (GNN) and Zhang neural network (ZNN) designs. Two major limitations should be overcome. The first limitation is the inapplicability of GNN models in time-varying environment, while the second constraint is the possibility of using the ZNN design only under the presence of invertible coefficient matrix. In this paper, by overcoming the possible limitations, we suggest, in all possible cases, a suitable solution for a consistent or inconsistent linear system. Convergence properties are investigated as well as exact solutions.
Katsikis, V. N., Mourtas, S. D., Stanimirović, P. S., Li, S., & Cao, X. (2021). Time-Varying Mean-Variance Portfolio Selection under Transaction Costs and Cardinality Constraint Problem via Beetle Antennae Search Algorithm (BAS). Operations Research Forum, 2(2), 18. presented at the 2021. Publisher's VersionAbstract
The Markowitz mean-variance portfolio selection is widely acclaimed as a very important investment strategy. A popular option to solve the static mean-variance portfolio selection (MVPS) problem is based on the use of quadratic programming (QP) methods. On the other hand, the static portfolio selection under transaction costs (PSTC) problem is usually approached with nonlinear programming (NLP) methods. In this article, we define and study the time-varying mean-variance portfolio selection under transaction costs and cardinality constraint (TV-MVPSTC-CC) problem as a time-varying nonlinear programming (TVNLP) problem. The TV-MVPSTC-CC also comprises the properties of a moving average. These properties make the TV-MVPSTC-CC an even greater analysis tool suitable to evaluate investments and identify trading opportunities across a continuous-time period. Using the Beetle Antennae Search (BAS) algorithm, we also provide an online solution to the static NLP problem. To the best of our knowledge, this is an innovative approach that incorporates modern meta-heuristic optimization techniques to provide an online, thus more realistic, solution to the TV-MVPSTC-CC problem. In this way, we present an online solution to a time-varying financial problem while eliminating the restrictions of static methods. Our approach is also verified by numerical experiments and computer simulations as an excellent alternative to traditional approaches.
Li, Z., Zhang, Y., Ming, L., Guo, J., & Katsikis, V. N. (2021). Real-Domain QR Decomposition Models Employing Zeroing Neural Network and Time-Discretization Formulas for Time-Varying Matrices. Neurocomputing. presented at the 2021. Publisher's VersionAbstract
This study investigated the problem of QR decomposition for time-varying matrices. We transform the original QR decomposition problem into an equation system using its constraints. Then, we propose a continuous-time QR decomposition (CTQRD) model by applying zeroing neural network method, equivalent transformations, Kronecker product, and vectorization techniques. Subsequently, a high-precision ten-instant Zhang et al discretization (ZeaD) formula is proposed. A ten-instant discrete-time QR decomposition model is also proposed by using the ten-instant ZeaD formula to discretize the CTQRD model. Moreover, three discrete-time QR decomposition models are proposed by applying three other ZeaD formulas, and three examples of QR decomposition are presented. The experimental results confirm the effectiveness and correctness of the proposed models for the QR decomposition of time-varying matrices.
Katsikis, V. N., Mourtas, S. D., Stanimirović, P. S., & Zhang, Y. (2021). Solving Complex-Valued Time-Varying Linear Matrix Equations via QR Decomposition With Applications to Robotic Motion Tracking and on Angle-of-Arrival Localization. IEEE Transactions on Neural Networks and Learning Systems, 1 - 10. Publisher's Version
2020
Mosić, D., Stanimirović, P. S., Sahoo, J. K., Behera, R., & Katsikis, V. N. (2020). One-sided weighted outer inverses of tensors. Journal of Computational and Applied Mathematics. presented at the 2020. Publisher's VersionAbstract
In this paper, for the first time in literature, we introduce one-sided weighted inverses and extend the notions of one-sided inverses, outer inverses and inverses along given elements. Although our results are new and in the matrix case, we decided to present them in tensor space with reshape operator. For this purpose, a left and right (M,N)-weighted (B,C)-inverse and the (M,N)-weighted (B,C)-inverse of a tensor are defined. Additionally, necessary and sufficient conditions for the existence of these new inverses are presented. We describe the sets of all left (or right) (M,N)-weighted (B,C)-inverses of a given tensor. As consequences of these results, we consider the one-sided (B,C)-inverse, (B,C)-inverse, one-sided inverse along a tensor and inverse along a tensor. Further, we introduce a (M,N)-weighted (B,C)-outer inverse and a W-weighted (B,C)-outer inverse of tensors with a few characterizations. Then, corresponding algorithms for computing various types of outer inverses of tensors are proposed, implemented and tested. The prowess of the proposed inverses are demonstrated for finding the solution of Poisson problem and the restoration of 3D color images.
Medvedeva, M., Simos, T. E., Tsitouras, C., & Katsikis, V. (2020). Direct estimation of SIR model parameters through second-order finite differences. Mathematical Methods in the Applied Sciences, n/a(n/a). presented at the 2020, John Wiley & Sons, Ltd. Publisher's VersionAbstract
SIR model is widely used for modeling the infectious diseases. This is a system of ordinary differential equations (ODEs). The numbers of susceptible, infectious, or immunized individuals are the compartments in these equations and change in time. Two parameters are the factor of differentiating these models. Here, we are not interested in solving the ODEs describing a certain SIR model. Given the observed data, we try to estimate the parameters that determine the model. For this, we propose a least squares approach using second-order centered differences for replacing the derivatives appeared in the ODEs. Then we arrive at a simple linear system that can be solved explicitly and furnish the approximations of the parameters. Numerical results over various artificial data verify the simplicity and accuracy of the new method.
Stanimirović, P. S., Katsikis, V. N., & Gerontitis, D. (2020). A New Varying-Parameter Design Formula for Solving Time-Varying Problems. Neural Processing Letters. presented at the 2020. Publisher's VersionAbstract
A novel finite-time convergent zeroing neural network (ZNN) based on varying gain parameter for solving time-varying (TV) problems is presented. The model is based on the improvement and generalization of the finite-time ZNN (FTZNN) dynamics by means of the varying-parameter ZNN (VPZNN) dynamics, and termed as VPFTZNN. More precisely, the proposed model replaces fixed and large values of the scaling parameter by an appropriate time-dependent gain parameter, which leads to a faster and bounded convergence of the error function in comparison to previous ZNN methods. The convergence properties of the proposed VPFTZNN dynamical evolution in its generic form is verified. Particularly, VPFTZNN for solving linear matrix equations and for computing generalized inverses are investigated theoretically and numerically. Moreover, the proposed design is applicable in solving the TV matrix inversion problem, solving the Lyapunov and Sylvester equation as well as in approximating the matrix square root. Theoretical analysis as well as simulation results validate the effectiveness of the introduced dynamical evolution. The main advantages of the proposed VPFTZNN dynamics are their generality and faster finite-time convergence with respect to FTZNN models.
Medvedeva, M.  A., Katsikis, V.  N., Mourtas, S.  D., & Simos, T. E. (2020). Randomized time-varying knapsack problems via binary beetle antennae search algorithm: Emphasis on applications in portfolio insurance. Mathematical Methods in the Applied Sciences. presented at the 2020, John Wiley & Sons, Ltd. Publisher's VersionAbstract
The knapsack problem is a problem in combinatorial optimization, and in many such problems, exhaustive search is not tractable. In this paper, we describe and analyze the randomized time-varying knapsack problem (RTVKP) as a time-varying integer linear programming (TV-ILP) problem. In this way, we present the on-line solution to the RTVKP combinatorial optimization problem and highlight the restrictions of static methods. In addition, the RTVKP is applied in the field of finance and converted into a portfolio insurance problem. Our methodology is confirmed by simulation tests in real-world data sets, in order to explain being an excellent alternative to traditional approaches.
Mosić, D., Stanimirović, P. S., & Katsikis, V. N. (2020). Solvability of some constrained matrix approximation problems using core-EP inverses. Computational and Applied Mathematics, 39(4), 311. presented at the 2020. Publisher's VersionAbstract
Using the core-EP inverse, we obtain the unique solution to the constrained matrix minimization problem in the Euclidean norm: $$\mathrm{Minimize }\ \Vert Mx-b\Vert _2$$Minimize‖Mx-b‖2, subject to the constraint $$x\in \mathcal{R}(M^k),$$x∈R(Mk),where $$M\in {\mathbb {C}}^{n\times n}$$M∈Cn×n, $$k=\mathrm {Ind}(M)$$k=Ind(M)and $$b\in {\mathbb {C}}^n$$b∈Cn. This problem reduces to well-known results for complex matrices of index one and for nonsingular complex matrices. We present two kinds of Cramer’s rules for finding unique solution to the above mentioned problem, applying one well-known expression and one new expression for core-EP inverse. Also, we consider a corresponding constrained matrix approximation problem and its Cramer’s rules based on the W-weighted core-EP inverse. Numerical comparison with classical strategies for solving the least squares problems with linear equality constraints is presented. Particular cases of the considered constrained optimization problem are considered as well as application in solving constrained matrix equations.
Katsikis, V. N., & Mourtas, S. D. (2020). Optimal Portfolio Insurance under Nonlinear Transaction Costs. Journal of Modeling and Optimization, 12(2), 117-124.
Khan, A. T., Cao, X., Li, S., Hu, B., & Katsikis, V. N. (2020). Quantum Beetle Antennae Search: A Novel Technique for The Constrained Portfolio Optimization Problem. SCIENCE CHINA Information Sciences. Science China Press.
Khan, A. H., Cao, X., Li, S., Katsikis, V. N., & Liao, L. (2020). BAS-ADAM: An ADAM based approach to improve the performance of beetle antennae search optimizer. IEEE/CAA Journal of Automatica Sinica, 7, 461–471. IEEE.
Sahoo, J. K., Behera, R., Stanimirović, P. S., & Katsikis, V. N. (2020). Computation of outer inverses of tensors using the QR decomposition. Computational and Applied Mathematics, 39, 1–20. Springer International Publishing.
Katsikis, V. N., Mourtas, S. D., Stanimirović, P. S., Li, S., & Cao, X. (2020). Time-varying minimum-cost portfolio insurance under transaction costs problem via Beetle Antennae Search Algorithm (BAS). Applied Mathematics and Computation, 385, 125453. Elsevier.
Gerontitis, D., Moysis, L., Stanimirović, P., Katsikis, V. N., & Volos, C. (2020). Varying-parameter finite-time zeroing neural network for solving linear algebraic systems. Electronics Letters, 56, 810–813. IET.
Sahoo, J. K., Behera, R., Stanimirović, P. S., Katsikis, V. N., & Ma, H. (2020). Core and core-EP inverses of tensors. Computational and Applied Mathematics, 39, 9. Springer International Publishing.
Stanimirović, P. S., Ćirić, M., Katsikis, V. N., Li, C., & Ma, H. (2020). Outer and (b, c) inverses of tensors. Linear and Multilinear Algebra, 68, 940–971. Taylor & Francis.
Khan, A. H., Cao, X., Katsikis, V. N., Stanimirović, P., Brajević, I., Li, S., Kadry, S., et al. (2020). Optimal Portfolio Management for Engineering Problems Using Nonconvex Cardinality Constraint: A Computing Perspective. IEEE Access, 8, 57437–57450. IEEE.
2019
Zhou, M., Chen, J., Stanimirović, P. S., Katsikis, V. N., & Ma, H. (2019). Complex Varying-Parameter Zhang Neural Networks for Computing Core and Core-EP Inverse. Neural Processing Letters, 1–31. Springer US.
Katsikis, V. N., & Mourtas, S. D. (2019). ORPIT: A Matlab Toolbox for Option Replication and Portfolio Insurance in Incomplete Markets. Computational Economics, 1–11. Springer US.
Ma, H., Li, N., Stanimirović, P. S., & Katsikis, V. N. (2019). Perturbation theory for Moore–Penrose inverse of tensor via Einstein product. Computational and Applied Mathematics, 38, 111. Springer International Publishing.
Katsikis, V. N., & Mourtas, S. D. (2019). A heuristic process on the existence of positive bases with applications to minimum-cost portfolio insurance in C [a, b]. Applied Mathematics and Computation, 349, 221–244. Elsevier.
Stanimirović, P. S., Katsikis, V. N., & Li, S. (2019). Integration enhanced and noise tolerant ZNN for computing various expressions involving outer inverses. Neurocomputing, 329, 129–143. Elsevier.
Stanimirović, P. S., Katsikis, V. N., & Kolundżija, D. (2019). Inversion and pseudoinversion of block arrowhead matrices. Applied Mathematics and Computation, 341, 379–401. Elsevier.
Stanimirović, P. S., Katsikis, V. N., Zhang, Z., Li, S., Chen, J., & Zhou, M. (2019). Varying-parameter Zhang neural network for approximating some expressions involving outer inverses. Optimization Methods and Software, 1–27. Taylor & Francis.
Stanimirović, P. S., Katsikis, V. N., Srivastava, S., & Pappas, D. (2019). A class of quadratically convergent iterative methods. Revista de la Real Academia de Ciencias Exactas, Fısicas y Naturales. Serie A. Matemáticas, 113, 3125–3146. Springer International Publishing.
Stanimirović, P. S., Kumar, A., & Katsikis, V. N. (2019). Further efficient hyperpower iterative methods for the computation of generalized inverses AT, S(2). Revista de la Real Academia de Ciencias Exactas, Fısicas y Naturales. Serie A. Matemáticas, 113, 3323–3339. Springer International Publishing.
2018
Stanimirović, P. S., Katsikis, V. N., & Li, S. (2018). Hybrid GNN-ZNN models for solving linear matrix equations. Neurocomputing, 316, 124–134. Elsevier.
Petković, M. D., Stanimirović, P. S., & Katsikis, V. N. (2018). Modified discrete iterations for computing the inverse and pseudoinverse of the time-varying matrix. Neurocomputing, 289, 155–165. Elsevier.
Pappas, D., Katsikis, V., & Stanimirovic, I. (2018). Symbolic computation of the Duggal transform. Journal of Linear and Topological Algebra (JLTA), 7, 53–62. Central Tehran Branch, Islamic Azad University.
Stanimirović, P. S., Katsikis, V. N., & Pappas, D. (2018). Computation of {2, 4} and {2, 3}-inverses based on rank-one updates. Linear and Multilinear Algebra, 66, 147–166. Taylor & Francis.
Pappas, D., Katsikis, V. N., & Stanimirović, P. S. (2018). The λ-Aluthge transform of EP matrices. Filomat, 32, 4403–4411.
2017
Srivastava, S., Stanimirović, P. S., Katsikis, V. N., & Gupta, D. K. (2017). A family of iterative methods with accelerated convergence for restricted linear system of equations. Mediterranean Journal of Mathematics, 14, 222. Springer International Publishing.
Pappas, D., Katsikis, V. N., & Stanimirović, I. P. (2017). Symbolic Computation of the Aluthge Transform. Mediterranean Journal of Mathematics, 14, 45. Springer International Publishing.
Stanimirovic, P., Pappas, D., & Katsikis, V. N. (2017). Minimization of quadratic forms and generalized inverses. Advances in Linear Algebra Research, 1.
Stanimirović, P. S., Katsikis, V. N., & Ma, H. (2017). Representations and properties of the W-weighted Drazin inverse. Linear and Multilinear Algebra, 65, 1080–1096. Taylor & Francis.
Chountasis, S., Pappas, D., & Katsikis, V. N. (2017). Signal watermarking in bi-dimensional representations using matrix factorizations. Computational and Applied Mathematics, 36, 341–357. Springer International Publishing.
Pappas, D., Katsikis, V. N., & Stanimirovic, I. P. (2017). Symbolic computation of the Aluthge transform.. Mediterr. J. Math.
2016
Katsikis, V. (2016). Applied Linear Algebra in Action. InTech Publications.
Katsikis, V. N. (2016). Computation of replicated exercise prices by using positive bases. Filomat, 30, 2973–2984. Faculty of Sciences and Mathematics, University of Niš.
Katsikis, V. N. (2016). A new computational method for finding the cheapest hedge. Facta Universitatis, Series: Mathematics and Informatics, 31, 349–362.
Katsikis, V. N. (2016). An alternative computational method for finding the minimum-premium insurance portfolio. In AIP Conference Proceedings (Vol. 1738, pp. 480020). AIP Publishing LLC.
Stanimirović, P. S., Katsikis, V. N., & Pappas, D. (2016). Computing $\{$2, 4$\}$ and $\{$2, 3$\}$-inverses by using the Sherman–Morrison formula. Applied Mathematics and Computation, 273, 584–603. Elsevier.
Stanimirović, P. S., Katsikis, V. N., & Stojanović, I. (2016). Computing the Pseudoinverse of Specific Toeplitz Matrices Using Rank-One Updates. Mathematical Problems in Engineering, 2016. Hindawi.
Katsikis, V. N., Papakostas, S. N., Tsitmidelis, S., & Tsitouras, C. (2016). Evolutionary generation of explicit two step methods for second order linear IVPs. In AIP Conference Proceedings (Vol. 1738, pp. 480038). AIP Publishing LLC.
2015
Stanimirović, P. S., Pappas, D., Katsikis, V. N., & Cvetković, M. S. (2015). Outer inverse restricted by a linear system. Linear and Multilinear Algebra, 63, 2461–2493. Taylor & Francis.
Stanimirović, P. S., Stojanović, I., Katsikis, V. N., Pappas, D., & Zdravev, Z. (2015). Application of the least squares solutions in image deblurring. Mathematical Problems in Engineering, 2015. Hindawi.
Stanimirović, P. S., Pappas, D., & Katsikis, V. N. (2015). Generalized inverse restricted by the normal Drazin equation. Linear and Multilinear Algebra, 63, 893–913. Taylor & Francis.
2014
Katsikis, V. N. (2014). A new computational tool for option replication. In 13th Serbian Mathematical Congress.
Tsitouras, C., & Katsikis, V. N. (2014). Bounds for variable degree rational L∞ approximations to the matrix cosine. Computer Physics Communications, 185, 2834–2840. North-Holland.
Tsitouras, C., & Katsikis, V. N. (2014). Solving undamped unforced free oscillators by L∞ approximations to cos. In AIP Conference Proceedings (Vol. 1618, pp. 824–827). American Institute of Physics.
2013
Katsikis, V. N. (2013). A Computational Study of Option Replication Based on Riesz Space Theory. Numerical Computations: Theory and Algorithms, 86.
Katsikis, V. N. (2013). A new characterization of markets that don't replicate any option through minimal-lattice subspaces. A computational approach.. Filomat, 27, 1357–1372. Faculty of Sciences and Mathematics, University of Niš.
2012
Katsikis, V. (2012). MATLAB: A fundamental tool for scientific computing and engineering applications. BoD–Books on Demand.
Chountasis, S., Katsikis, V. N., & Pappas, D. (2012). Image reconstruction methods for MATLAB users—a Moore-Penrose inverse approach. MATLAB—A Fundamental Tool for Scientific Computing and Engineering Applications, 1.
Katsikis, V. N. (2012). MATLAB aided option replication. MATLAB-A Fundamental Tool for Scientific Computing and Engineering Applications, 3, 179–194.
Stanimirović, P. S., Pappas, D., Katsikis, V. N., & Stanimirović, I. P. (2012). Symbolic computation of AT, S (2)-inverses using QDR factorization. Linear Algebra and its Applications, 437, 1317–1331. North-Holland.
Stanimirović, P. S., Pappas, D., Katsikis, V. N., & Stanimirović, I. P. (2012). Full-rank representations of outer inverses based on the QR decomposition. Applied Mathematics and Computation, 218, 10321–10333. Elsevier.
Chountasis, S., Katsikis, V. N., Pappas, D., & Perperoglou, A. (2012). Reconstruction of radar signals using the Whittaker smoother and the Moore-Penrose inverse. Applied Mathematical Sciences, 6, 1205 - 1219.
Chountasis, S., Katsikis, V. N., Pappas, D., & Perperoglou, A. (2012). The whittaker smoother and the moore-penrose inverse in signal reconstruction. Applied Mathematical Sciences, 6, 1205–1219.
Katsikis, V. N., & Polyrakis, I. A. (2012). Computation of vector sublattices and minimal lattice-subspaces of Rk: Applications in finance. Applied Mathematics and Computation, 218, 6860–6873. Elsevier.
2011
Katsikis, V. N. (2011). Computational methods for option replication. International Journal of Computer Mathematics, 88, 2752–2769. Taylor & Francis.
Katsikis, V. N., Pappas, D., & Petralias, A. (2011). An improved method for the computation of the Moore–Penrose inverse matrix. Applied Mathematics and Computation, 217, 9828–9834. Elsevier.
Katsikis, V., & Pappas, D. (2011). The restricted weighted generalized inverse of a matrix. The Electronic Journal of Linear Algebra, 22.
2010
Katsikis, V. N. (2010). Computational and Mathematical Methods in Portfolio Insurance. A MATLAB-Based Approach., Matlab-Modelling, Programming and Simulations, ISBN: 978-953-307-125-1. InTech, 2010 (Book chapter).
Chountasis, S., Katsikis, V. N., & Pappas, D. (2010). Digital image reconstruction in the spectral domain utilizing the Moore-Penrose inverse. Mathematical Problems in Engineering, 2010. Hindawi.
Chountasis, S., Katsikis, V. N., & Pappas, D. (2010). Moore-Penrose Inverse Digital Image Reconstruction in the Spectral Domain Utilizing the Volume 2010, Article ID 750352, 14 pages. Mathematical Problems in Engineering, 2010.
Katsikis, V. N. (2010). Computational and mathematical methods in portfolio insurance-A MATLAB-based approach. Matlab–Modelling, Programming and Simulations. InTech, Rijeka, Croatia.
2009
Chountasis, S., Pappas, D., & Katsikis, V. N. (2009). Image restoration via fast computing of the Moore-Penrose inverse matrix. In 2009 16th International Conference on Systems, Signals and Image Processing (pp. 1–4). IEEE.
Katsikis, V. N. (2009). The Riesz Interpolation Property for the Space of Continuously Differentiable Functions. Int. J. Contemp. Math. Sciences, 4, 799–802.
Chountasis, S., Katsikis, V. N., & Pappas, D. (2009). Applications of the Moore-Penrose inverse in digital image restoration. Mathematical Problems in Engineering, 2009. Hindawi.
Katsikis, V. N. (2009). A Matlab-based rapid method for computing lattice-subspaces and vector sublattices of Rn: Applications in portfolio insurance. Applied Mathematics and Computation, 215, 961–972. Elsevier.
2008
Katsikis, V. N. (2008). Additive Mappings between Directed Wedges with the Riesz Interpolation Property. Int. Journal of Math. Analysis, 2, 11-25.
Katsikis, V. N. (2008). Computational methods in lattice-subspaces of C [a, b] with applications in portfolio insurance. Applied Mathematics and Computation, 200, 204–219. Elsevier.
Katsikis, V., & Pappas, D. (2008). Fast computing of the Moore-Penrose inverse matrix. The Electronic Journal of Linear Algebra, 17, 637–650.
Katsikis, V. N. (2008). Methods on Computing Positive Bases in Finite-Dimensional Vector Sublattices. Applications in Completion of Security Markets and in the Theory of Efficient Funds.. In AIP Conference Proceedings (Vol. 1048, pp. 302–306). American Institute of Physics.
2007
Katsikis, V. N. (2007). Generalized wedges and ordered spaces with the Riesz decomposition property. Nonlinear Functional Analysis and Applications.
Katsikis, V. N. (2007). Computational methods in portfolio insurance. Applied Mathematics and Computation, 189, 9–22. Elsevier.
2006
Katsikis, V.  N., & Polyrakis, I. A. (2006). Positive bases in ordered subspaces with the Riesz decomposition property. Studia Mathematica, 174, 233–253. Institute of Mathematics Polish Academy of Sciences.