Linear programming with positive semi-definite matrices (Q1286269)

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.