arXiv subjects

R. Jana

Publications and source records attributed to R. Jana.

6 recordsLinked to original sources

arXiv2021

Bounded Homotopy Path Approach to Find the Solution of Linear Complementarity Problems

In this article, we introduce a new homotopy function to trace the trajectory by applying modified homotopy continuation method for finding the solution of the linear complementarity problem. Earlier several authors attempted to propose homotopy functions based on original problems. We propose the homotopy function based on the Karush-Kuhn-Tucker condition of the corresponding quadratic programming problem. The proposed approach extends the processability of the larger class of linear complementarity problem and overcomes the limitations of other existing homotopy approaches. We show that the homotopy path approaching the solution is smooth and bounded with positive tangent direction of the homotopy path. Various classes of numerical examples are illustrated to show the effectiveness of the proposed algorithm and the superiority of the algorithm among other existing iterative methods.

math.OC↗

arXiv2021

On Column Competent Matrices and Linear Complementarity Problem

We revisit the class of column competent matrices and study some matrix theoretic properties of this class. The local $w$-uniqueness of the solutions to the linear complementarity problem can be identified by the column competent matrices. We establish some new results on $w$-uniqueness properties in connection with column competent matrices. These results are significant in the context of matrix theory as well as algorithms in operations research. We prove some results in connection with locally $w$-uniqueness property of column competent matrices. Finally we establish a connection between column competent matrices and column adequate matrices with the help of degree theory.

math.OC↗

arXiv2019

On Semimonotone Star Matrices and Linear Complementarity Problem

In this article, we introduce the class of semimonotone star ($E_0^s$) matrices. We establish the importance of the class of $E_0^s$-matrices in the context of complementarity theory. We show that the principal pivot transform of $E_0^s$-matrix is not necessarily $E_0^s$ in general. However, we prove that $\tilde{E_0^s}$-matrices, a subclass of the $E_0^s$-matrices with some additional conditions, is in $E_0^f$ by showing this class is in $P_0.$ We prove that LCP$(q, A)$ can be processable by Lemke's algorithm if $A\in \tilde{E_0^s}\cap P_0.$ We find some conditions for which the solution set of LCP$(q, A)$ is bounded and stable under the $\tilde{E^s_0}$-property. We propose an algorithm based on an interior point method to solve LCP$(q, A)$ given $A \in \tilde{E^{s}_{0}}.$

math.OC↗

arXiv2019

More On Hidden $Z$-Matrices and Linear Complementarity Problem

In this article we study linear complementarity problem with hidden $Z$-matrix. We extend the results of Fiedler and Pt{á}k for the linear system in complementarity problem using game theoretic approach. We establish a result related to singular hidden $Z$-matrix. We show that for a non-degenerate feasible basis, linear complementarity problem with hidden $Z$-matrix has unique non-degenerate solution under some assumptions. The purpose of this paper is to study some properties of hidden $Z$-matrix.

math.OC↗

arXiv2018

Iterative Descent Method for Generalized Leontief Model

In this paper we consider generalized Leontief model. We show that under certain condition the generalized Leontief model is solvable by iterative descent method based on infeasible interior point algorithm. We prove the convergence of the method from strictly positive starting point. A numerical example is presented to demonstrate the performance of the algorithm

math.OC↗

arXiv2018

Some Aspects on Solving Transportation Problem

In this paper, we consider a class of transportation problems which arises in sample surveys and other areas of statistics. The associated cost matrices of these transportation problems are of special structure. We observe that the optimality of North West corner solution holds for the general problem where cost component is replaced by a convex function. We revisit assignment problem and present a weighted version of K$\ddot{o}$nig-Egerv$\acute{a}$ry theorem and Hungarian method. The weighted Hungarian method proposed in the paper can be used for solving transportation problem.

math.OC↗