On Semimonotone Star Matrices and Linear Complementarity Problem

2018/08/01 by R. Jana, Rajkumar Jana, Jana, R. +6
Computer Science · Engineering · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC) #graph theory and CDMA systems #math.OC

paper · pdf · doi:10.48550/arxiv.1808.00281

openalex publication_date 2018/08/01 · arxiv created 2019/09/09 · arxiv updated 2019/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we introduce the class of semimonotone star (E₀^s) matrices. We establish the importance of the class of E₀^s-matrices in the context of complementarity theory. We show that the principal pivot transform of E₀^s-matrix is not necessarily E₀^s in general. However, we prove that E₀^s-matrices, a subclass of the E₀^s-matrices with some additional conditions, is in E₀^f by showing this class is in P₀. We prove that LCP(q, A) can be processable by Lemke's algorithm if A∈ E₀^s∩ P₀. We find some conditions for which the solution set of LCP(q, A) is bounded and stable under the E^s₀-property. We propose an algorithm based on an interior point method to solve LCP(q, A) given A ∈ E^s₀.

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