An optimality test for semi-infinite linear programming

In this paper the authors present a test to characterize the optimal solutions for the continuous semi-infinite linear programming problem. This optimality characterization is a condition of Karush-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. The authors give some illustrative examples. They show that the local Mangasarian-Fromovitz constraint qualification is almost equivalent to Slater qualification for this problem. Furthermore, it follows from the present study that this optimality condition is always necessary for a wide class of semi-infinite linear programming problems.