Mathematical Problems in Engineering
Volume 2 (1996), Issue 6, Pages 499-522
Linear programming with positive semi-definite matrices
LAAS-CNRS, 7 Avenue du Colonel Roche, Toulouse Cédex 31 077, France
Received 31 July 1995
Copyright © 1996 J. B. Lasserre. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We consider the general linear programming problem over the cone of positive semi-definite 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.