An optimality test for semi-infinite linear programming

Abstract

In this paper we present a test to characterize the optimal solutions for the continuous semi-infinite linear programming problem. This optimality characterization is a condition of Kuhn–Tucker type. The resolution of a linear program permits to check the optimality of a feasible point,to detect the unboundedness of the problem and to find descent directions. We give some illustrative examples. We show that the local Mangasarian–Fromovitz constraint qualification is almost equivalent to Slater qualification for this problem. Furthermore, it follows from our study that this optimality condition is always necessary for a wide class of semi-infinite linear programming problems

Keywords:

• Linear Programs
• Semi-Infinite Programming
• Optimality Conditions
• Constraint Qualifications