Predrag Stanimirovic

University of Niš | NIS · Faculty of Sciences and Mathematics (PMF)

An improved activation function, termed extended sign-bi-power (Esbp), is proposed. An extension of the Li zeroing neural network (ELi-ZNN) based on the Esbp activation is derived to obtain the online solution of the time-varying inversion problem. A detailed theoretical analysis confirms that the new activation function accomplishes fast convergen...

This chapter is devoted to \textcolor{red}{the survey of} quaternion restricted two-sided matrix equation $\mathbf{AXB}=\mathbf{D}$ and approximation problems related with it. Unique solutions to the considered approximation matrix problems and the restricted quaternion two-sided matrix equations with specific constraints are expressed in terms of...

The main goal of this chapter is to present necessary and sufficient conditions for the existence and representations of solutions to some restricted matrix equations and the systems of matrix equations. In particular, equivalent conditions for the existence and representations of $\{2\}$-, $\{1\}$-, and $\{1,2\}$-inverses with additional assumptio...

Application of generalized inverses in solving the inverse model control-oriented minimum-energy perfect control design (PCD) problem for linear time-invariant multi-input/multi-output systems governed by the discrete-time $d$-state-space structure is presented in this paper. For this reason, an appropriate class of polynomial generalized inverses...

This paper investigates the refined perturbation formulae and perturbation bounds for the group inverse and its oblique projection by the Schur decomposition. In addition, relative perturbation formulae and bounds of some rational expressions that involve group inverses of initial and perturbed matrix are considered. The obtained perturbation limit...

Special Issue Information Dear Colleagues, Intelligent computing has greatly expanded the scope of computing, extending it from traditional computing on data to increasingly heterogeneous computing paradigms. At the same time, the majority of machine-learning methods are based on optimization theory and optimization algorithms, minimizing the inter...

We investigate a solution of a convex programming problem with a strongly convex objective function based on the dual approach. A dual optimization problem has constraints on the positivity of variables. We study the methods and properties of transformations of dual variables that enable us to obtain an unconstrained optimization problem. We invest...

It is well known that minimum-cost portfolio insurance (MPI) is an essential investment strategy. This article presents a time-varying version of the original static MPI problem, which is thus more realistic. Then, to solve it efficiently, we propose a powerful recurrent neural network called the linear-variational-inequality primal-dual neural net...

This paper presents a dynamic model based on neutrosophic numbers and a neutrosophic logic engine. The introduced neutrosophic logic/fuzzy adaptive Zeroing Neural Network dynamic is termed NSFZNN and represents an improvement over the traditional Zeroing Neural Network (ZNN) design. The model aims to calculate the matrix pseudo-inverse and the mini...

https://www.mdpi.com/journal/symmetry/special_issues/W4C4SF306N

Dear Colleagues, The subject convex analysis is very important in the theoretical aspects of mathematics and also for economists and physicists. Mathematicians use this theory, to provide the solution to problems that arise in mathematics. This theory touches almost all branches of mathematics. Convex functions play an important role in many area...

The solvability of several new constrained quaternion matrix equations is investigated, and their unique solutions are presented in terms of the weighted MPD inverse and weighted DMP inverse of suitable matrices. It is interesting to consider some exceptional cases of these new equations and corresponding solutions. Determinantal representations fo...

This research proposes and investigates some improvements in gradient descent iterations that can be applied for solving system of nonlinear equations (SNE). In the available literature, such methods are termed improved gradient descent methods. We use verified advantages of various accelerated double direction and double step size gradient methods...

The influence of neutrosophy on many fields of science and technology, as well as its numerous applications, are evident. Our motivation is to apply neutrosophy for the first time in order to improve methods for solving unconstrained optimization. Particularly, in this research, we propose and investigate an improvement of line search methods for s...

We provide existence criteria and characterizations for outer inverses in a semigroup belonging to the prescribed Green’s ℛ-, ℒ- and ℋ-classes. These results generalize the well-known problem of finding outer inverses of a matrix over a field with the prescribed range or/and null space.We show that Mary’s inverse along an element, Drazin’s (b, c)-i...

We establish a relaxation subgradient method (RSM) that includes parameter optimization using rank-two correction of metric matrices with a structure similar to that in quasi-Newtonian (QN) methods. The metric matrix transformation consists in suppressing orthogonal and amplifying collinear components of the minimum-length subgradient vector. The p...

Engineering design optimization problems are difficult to solve because the objective function is often complex, with a mix of continuous and discrete design variables and various design constraints. Our research presents a novel hybrid algorithm that integrates the benefits of the sine cosine algorithm (SCA) and artificial bee colony (ABC) to addr...

The paper proposes a novel nature-inspired optimization technique called Eagle Perching Optimizer (EPO). It is an addition to the family of swarm-based meta-heuristic algorithms. It mimics eagles’ perching nature to find prey (food). The EPO is based on the exploration and exploitation of an eagle when it descends from the height such that it formu...

Many researchers have addressed problems involving time-varying (TV) general linear matrix equations (GLMEs) because of their importance in science and engineering. This research discusses and solves the topic of solving TV GLME using the zeroing neural network (ZNN) design. Five new ZNN models based on novel error functions arising from gradient-d...

Many practical applications in applied sciences such as imaging, signal processing, and motion control can be reformulated into a system of nonlinear equations with or without constraints. In this paper, a new descent projection iterative algorithm for solving a nonlinear system of equations with convex constraints is proposed. The new approach is...

This article proposes an optimal value for the scaled Perry conjugate gradient (CG) method, which aims to solve large-scale monotone nonlinear equations. An optimal choice for the scaled parameter is obtained by minimizing the largest and smallest eigenvalues of the search direction matrix. In addition, the corresponding Perry CG parameter is incor...

Competition is considered to be a driving force of many swarm systems in maintaining vitality, as important as collaboration. To model this competitive nature, an operation called k-winner-take-all (kWTA) is introduced that can output k maximum values from p input signals with p⩽k≤1. In this paper, different projection functions (PFs) are combined...

In this work, we consider the problem of calculating the generalized Moore–Penrose inverse, which is essential in many applications of graph theory. We propose an algorithm for the massively parallel systems based on the recursive algorithm for the generalized Moore–Penrose inverse, the generalized Cholesky factorization, and Strassen’s matrix inve...

This paper investigates new solution sets for the Yang–Baxter-like (YB-like) matrix equation involving constant entries or rational functional entries over complex numbers. Towards this aim, first, we introduce and characterize an essential class of generalized outer inverses (termed as {2, 5}-inverses) of a matrix, which commute with it. This clas...

A robust noise-tolerant zeroing neural network (ZNN) is introduced for solving time-varying linear matrix equations (TVLME). The convergence speed of designed neural dynamics is analyzed theoretically and compared with the convergence of neural networks which include traditional activation functions, such as the tunable activation function, versati...

In current study, the modified variational iteration algorithm-I is investigated in the form of the analytical and numerical treatment of different types of nonlinear partial differential equations modelling physical phenomena where particles, energy, or other physical quantities are transferred inside a physical system due to two processes: diffus...

Following the popularity of the core-EP (c-EP) and weighted core-EP (w-c-EP) inverses, so called one-sided versions of the w-c-EP inverse are introduced recently in Behera et al. (Results Math 75:174 (2020). These extensions are termed as E-w-c-EP and F-w-d-c-EP g-inverses as well as the star E-w-c-EP and the F-w-d-c-EP star classes of g-inverses....

A modified Dai-Liao type conjugate gradient method for solving large-scale nonlinear systems of monotone equations is introduced and investigated in actual research. The starting point is the Dai-Liao type conjugate gradient method which is based on the descent Dai-Liao method and the hyperplane projection technique, known as the Dai-Liao projectio...

This research aims to introduce and investigate the right and left W-MPCEP, W-CEPMP, and W-MPCEPMP generalized inverses for quaternion matrices. These generalized inverses are introduced as extensions of corresponding generalized inverses applicable to complex matrices. Some new characterizations and expressions of these inverses are presented. Det...

The intention of our research is to define and investigate some extensions of generalized core-EP (or shortly GCEP) inverse. Inspired by Urquhart expression for the outer inverses, we firstly introduce Φ1-GCEP inverse replacing AR(B),N(C)(2) in the definition of the GCEP inverse by the more general expression Φ1:=B(CAB)(1)C. Further, Φ2-GCEP invers...

This research introduces three novel zeroing neural network (ZNN) models for addressing the time-varying Yang–Baxter-like matrix equation (TV-YBLME) with arbitrary (regular or singular) real time-varying (TV) input matrices in continuous time. One ZNN dynamic utilizes error matrices directly arising from the equation involved in the TV-YBLME. Moreo...

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 o...

In the context of infinite-horizon optimal control problems, the algebraic Riccati equations (ARE) arise when the stability of linear time-varying (LTV) systems is investigated. Using the zeroing neural network (ZNN) approach to solve the time-varying eigendecomposition-based ARE (TVE-ARE) problem, the ZNN model (ZNNTVE-ARE) for solving the TVE-ARE...

An extension of the Integrated Simple Weighted Sum Product (WISP) method is presented in this article, customized for the application of single-valued neutrosophic numbers. The extension is suggested to take advantage that the application of neutrosophic sets provides in terms of solving complex decision-making problems, as well as decision-making...

Various forms of the algebraic Riccati equation (ARE) have been widely used to investigate the stability of nonlinear systems in the control field. In this paper, the time-varying ARE (TV-ARE) and linear time-varying (LTV) systems stabilization problems are investigated by employing the zeroing neural networks (ZNNs). In order to solve the TV-ARE p...

Expressions which include the Moore-Penrose (MP) inverse with various generalized inverses have been popular topic in numerical linear algebra. The most general case was the combination of the MP inverse with outer inverses $A^{(2)}_{\R(B),\N(C)}$, known as the composite outer inverses. Starting from well-known and useful Urquhart representation of...

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...

The formation of patterns is one of the main stages in logical data analysis. Fuzzy approaches to pattern generation in logical analysis of data allow the pattern to cover not only objects of the target class, but also a certain proportion of objects of the opposite class. In this case, pattern search is an optimization problem with the maximum cov...

Among the localization algorithms of wireless sensor networks (WSNs), the distance vector-hop (DV-Hop) algorithm has been widely concerned thanks to its simplicity, low hardware requirements, and easy implementation. However, the localization accuracy of the DV-Hop algorithm declines greatly when the sensor nodes are unevenly distributed. To improv...

The notions of the MPCEP inverse and ∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$*$$\end{document}CEPMP inverse are expanded to quaternion matrices and their deter...

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 e...

This paper investigates convergence properties of gradient neural network (GNN) and GNN-based dynamical systems for computing generalized inverses. The main results are exact analytical solutions for the state matrices of the corresponding GNN and GNN-based dynamical systems. The exact solutions are given in each time instant, which enables to expr...

Hyperpower family of iterative methods of arbitrary convergence order is one of the most frequently applied methods for approximating the matrix inverse and generalized inverses. On the * Complimentary Contributor Copy 208 V. N. Katsikis, P. S. Stanimirović, S. D. Mourtas et al. other hand, Zeroing neural network (ZNN) is a kind of neural dynamics...

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 probl...

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. Bas...

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...

Various novel expressions of weak core inverse and its dual are developed in this paper. In addition, integral and limit representations as well as perturbation formulae for the weak core and dual weak core inverses are presented. We investigate continuity for the weak core inverse and its dual. The weak core and dual weak core inverses for upper b...

In this paper, as a generalization of Urquhart's formulas, we present a full description of the sets of inner inverses and (B,C)-inverses over an arbitrary field. In addition, identifying the matrix-vector space with an affine space, we analyse geometrical properties of the main generalized inverse sets. We prove that the set of inner inverses, and...

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....

A correlation between fuzzy logic systems (FLS) and zeroing neural networks (ZNN) design is investigated. It is shown that the gain parameter included in ZNN design can be dynamically adjusted over time by means of an appropriate value derived as the output of a properly defined FLS which includes appropriately defined membership functions and fuzz...

A family of varying-parameter finite-time zeroing neural networks (VPFTZNN) is introduced for solving the time-varying Sylvester equation (TVSE). The convergence speed of the proposed VPFTZNN family is analysed and compared with the traditional zeroing neural network (ZNN) and the finite-time zeroing neural network (FTZNN). The behaviour of the pro...

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...

We introduce three kinds of new weighted quaternion-matrix minimization problems in order to extend some well-known constrained approximation problems. The main result is the claim that these new minimization problems have unique solutions which are expressed in terms of expressions involving weighted core-EP inverse and its dual for adequate quate...

We consider the solvability of four new restricted quaternion matrix equations (QME) and prove that these equations have the unique solutions determined by adequate MPD and DMP inverses. Several particular cases of these equations are presented too. Determinantal representations of solutions to new constrained equations and their particular cases a...

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 determin...

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 determina...

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....

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....

As a special type of neurodynamic methodology dedicated to finding zeros of equations, zeroing neurodynamics has shown a powerful ability in solving challenging online time-varying problems. Multi-linear systems, on the other hand, are a type of tensor equations with a wide range of applications. In this paper, a zeroing neurodynamics approach for...

Dear Colleagues, This Special Dedication Issue includes the theories and applications of the areas developed and advanced by Professor Ji-Huan He and his research collaborators, mainly summarized in the list of keywords: Two-Scale Fractal Calculus; text Fractional Calculus; Variational Iteration Method; He’s Fractal Derivative; He’s Fractional Der...

This paper presents a new method of steganography based on a combination of Catalan objects and Voronoi–Delaunay triangulation. Two segments are described within the proposed method. The first segment describes the process of embedding data and generating a complex stego key. The second segment explains the extraction of a hidden message. The main...

In this paper, we introduce the notion of outer generalized inverses, with predefined range and null space, of tensors with rational function entries equipped with the Einstein product over an arbitrary field, of characteristic zero, with or without involution. We assume that the involved tensor entries are rational functions of unassigned variable...

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)-weig...

The aim of this paper is to provide new representations and characterizations of the weak group inverse. We give a relation between the weak group inverse and a corresponding nonsingular border matrix. Continuity of weak group inverse is studied. Several limit representations, integral representations and perturbation formulae for the weak group in...

This paper investigates representations of outer matrix inverses with prescribed range and/or null space in terms of inner inverses. Further, required inner inverses are com- puted as solutions of appropriate linear matrix equations (LME). In this way, algorithms for computing outer inverses are derived using solutions of appropriately defined LME....

New properties and representations for the core-EP inverse are developed. Particularly, the core-EP inverse of an upper triangular matrix and its sign pattern are considered. Determi- nantal representations for the core-EP inverse and core-EP solution of linear systems are investigated. Corresponding representations of the weighted core-EP inverse...

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 net- work (ZNN) designs. Two major limitations should be overcome. The first limitation is the inapplicability of GNN models in time-varying environment, while the second cons...

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 usua...

A special recurrent neural network (RNN), that is the zeroing neural network (ZNN), is adopted to find solutions to time‐varying quadratic programming (TVQP) problems with equality and inequality constraints. However, there are some weaknesses in activation functions of traditional ZNN models, including convex restriction and redundant formulation....