J. B. Lasserre, "Linear programming with positive semi-definite matrices", Mathematical Problems in Engineering, vol. 2, Article ID 749783, 24 pages, 1996. https://doi.org/10.1155/S1024123X96000452
Linear programming with positive semi-definite matrices
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.
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