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A MODIFICATION OF GRADIENT METHOD OF CONVEX PROGRAMMING AND ITS IMPLEMENTATION
Stanimirovic, Predrag S.,Tasic, Milan B. 한국전산응용수학회 2004 Journal of applied mathematics & informatics Vol.16 No.1
A modification of the gradient method of convex programming is introduced. Also, we describe symbolic implementation of the gradient method and its modification by means of the programming language MATHEMATICA. A few numerical examples are reported.
FIRST ORDER GRADIENT OPTIMIZATION IN LISP
Stanimirovic, Predrag,Rancic, Svetozar 한국전산응용수학회 1998 Journal of applied mathematics & informatics Vol.5 No.3
In this paper we develop algorithms in programming lan-guage SCHEME for implementation of the main first order gradient techniques for unconstrained optimization. Implementation of the de-scent techniques which use non-optimal descent steps as well as imple-mentation of the optimal descent techniques are described. Also we investigate implementation of the global problem called optimization along a line. Developed programs are effective and simpler with re-spect to the corresponding in the procedural programming languages. Several numerical examples are reported.
COMPUTING GENERALIZED INVERSES OF A RATIONAL MATRIX AND APPLICATIONS
Stanimirovic, Predrag S.,Karampetakis, N. P.,Tasic, Milan B. 한국전산응용수학회 2007 Journal of applied mathematics & informatics Vol.24 No.1
In this paper we investigate symbolic implementation of two modifications of the Leverrier-Faddeev algorithm, which are applicable in computation of the Moore-Penrose and the Drazin inverse of rational matrices. We introduce an algorithm for computation of the Drazin inverse of rational matrices. This algorithm represents an extension of the papers [11] and [14]. and a continuation of the papers [15, 16]. The symbolic implementation of these algorithms in the package MATHEMATICA is developed. A few matrix equations are solved by means of the Drazin inverse and the Moore-Penrose inverse of rational matrices.
COMPUTING DETERMINANTAL REPRESENTATION OF GENERALIZED INVERSES
Stanimirovic, Predrag-S.,Tasic, Milan-B. 한국전산응용수학회 2002 The Korean journal of computational & applied math Vol.9 No.2
We investigate implementation of the determinantal representation of generalized inverses for complex and rational matrices in the symbolic package MATHEMATICA. We also introduce an implementation which is applicable to sparse matrices.
COMPUTING DETERMINANTAL REPRESENTATION OF GENERALIZED INVERSES
Predrag S. Stanimirovic,Milan B. Tasic 한국전산응용수학회 2002 Journal of applied mathematics & informatics Vol.9 No.2
We investigate implementation of the determinantal representationof generalized inverses for complex and rational matricesin the symbolic package {ssr MATHEMATICA}.We also introduce an implementation which is applicable to sparse matrices.
A modification of gradient method of convex programming and its implementation
P. S. Stanimirovic,Milan B. Tasic 한국전산응용수학회 2004 Journal of applied mathematics & informatics Vol.16 No.-
A modification of the gradient method of convex programming is introduced. Also, we describe symbolic implementation of the gradient method and its modification by means of the programming language MATHEMATICA. A few numerical examples are reported.
SINGULAR CASE OF GENERALIZED FIBONACCI AND LUCAS MATRICES
Miladinovic, Marko,Stanimirovic, Predrag Korean Mathematical Society 2011 대한수학회지 Vol.48 No.1
The notion of the generalized Fibonacci matrix $\mathcal{F}_n^{(a,b,s)}$ of type s, whose nonzero elements are generalized Fibonacci numbers, is introduced in the paper [23]. Regular case s = 0 is investigated in [23]. In the present article we consider singular case s = -1. Pseudoinverse of the generalized Fibonacci matrix $\mathcal{F}_n^{(a,b,-1)}$ is derived. Correlations between the matrix $\mathcal{F}_n^{(a,b,-1)}$ and the Pascal matrices are considered. Some combinatorial identities involving generalized Fibonacci numbers are derived. A class of test matrices for computing the Moore-Penrose inverse is presented in the last section.
ALGORITHM FOR WEBER PROBLEM WITH A METRIC BASED ON THE INITIAL FARE
Kazakovtsev, Lev A.,Stanimirovic, Predrag S. The Korean Society for Computational and Applied M 2015 Journal of applied mathematics & informatics Vol.33 No.1
We introduce a non-Euclidean metric for transportation systems with a defined minimum transportation cost (initial fare) and investigate the continuous single-facility Weber location problem based on this metric. The proposed algorithm uses the results for solving the Weber problem with Euclidean metric by Weiszfeld procedure as the initial point for a special local search procedure. The results of local search are then checked for optimality by calculating directional derivative of modified objective functions in finite number of directions. If the local search result is not optimal then algorithm solves constrained Weber problems with Euclidean metric to obtain the final result. An illustrative example is presented.
Algorithm for Weber problem with a metric based on the initial fare
Lev A. Kazakovtsev,Predrag S. Stanimirovic 한국전산응용수학회 2015 Journal of applied mathematics & informatics Vol.33 No.1
We introduce a non-Euclidean metric for transportation systems with a defined minimum transportation cost (initial fare) and investigatethe continuous single-facility Weber location problem based on this metric. The proposed algorithm uses the results for solving the Weber problem with Euclidean metric by Weiszfeld procedure as the initial point fora special local search procedure. The results of local search are then checked for optimality by calculating directional derivative ofmodified objective functions in finite number of directions. If the local search result is not optimal then algorithm solves constrainedWeber problems with Euclidean metric to obtain the final result. An illustrative example is presented.