Mathematical Problems in Engineering

Mathematical Problems in Engineering / 1996 / Article

Open Access

Volume 2 |Article ID 749783 |

J. B. Lasserre, "Linear programming with positive semi-definite matrices", Mathematical Problems in Engineering, vol. 2, Article ID 749783, 24 pages, 1996.

Linear programming with positive semi-definite matrices

Received31 Jul 1995


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.

Copyright © 1996 Hindawi Publishing Corporation. 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.

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