Linear programming with positive semi-definite matrices
type: Item
instance of: scholarly article
title: Linear programming with positive semi-definite matrices
zbMATH Open document ID: 0919.90108
DOI: 10.1155/S1024123X96000452
published in: Mathematical Problems in Engineering
publication date: 1999-05-03T00:00:00Z
full work available at URL: https://eudml.org/doc/48215
review text: Summary: We consider the general linear programming problem over the cone of positive semidefinite matrices. We first provide a simple sufficient condition for existence of optimal solutions and absence of a duality gap without requiring existence of a strictly feasible solution. We then simply characterize the analogues of the standard concepts of linear programming, i.e., extreme points, basis, reduced cost, degeneracy, pivoting step as well as a simplex-like algorithm.
Mathematics Subject Classification ID: 90C05
zbMATH DE Number: 1283606
zbMATH Keywords: cone of positive semidefinite matrices
zbMATH Keywords: sufficient condition
zbMATH Keywords: existence of optimal solutions
zbMATH Keywords: duality gap
zbMATH Keywords: simplex-like algorithm
author: Jean B. Lasserre
MaRDI profile type: Publication
OpenAlex ID: W2099235735
description: scientific article; zbMATH DE number 1283606