On the uniqueness of the optimal solution in linear programming

Abstract

In this paper numerous necessary and sufficient conditions will be given for a vector to be the unique optimal solution of the primal problem, as well as for that of the dual problem, and even for the case when the primal and the dual problem have unique optimal solutions at the same time, respectively, by means of using the strict complementarity and the linear independence constraint qualification. Beyond that, the topological structure of the optimal solutions satisfying the strict complementarity will be determined.