Title :
Linear programming with positive semi definite matrices
Author :
Lasserre, Jean B.
Author_Institution :
Lab. d´´Autom. et d´´Anal. des Syst., CNRS, Toulouse, France
Abstract :
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
Keywords :
convergence of numerical methods; duality (mathematics); linear programming; matrix algebra; convergence; degeneracy; duality; extreme points; linear programming; matrix algebra; pivoting step; positive semi definite matrices; simplex-like algorithm; sufficient condition; Control theory; Cost function; Eigenvalues and eigenfunctions; Hilbert space; Linear programming; Sufficient conditions; Symmetric matrices; Vectors;
Conference_Titel :
Decision and Control, 1995., Proceedings of the 34th IEEE Conference on
Conference_Location :
New Orleans, LA
Print_ISBN :
0-7803-2685-7
DOI :
10.1109/CDC.1995.480242