Generalized corner optimal solution for LSIP: existence and numerical computation

In this paper, we consider general linear semi-infinite programming (LSIP) problems and study the existence and computation of optimal solutions at special generalized corner points called generalized ladder points (glp). We develop conditions, including an equivalent condition, under which glp optimal solutions exist. These results are fundamentally important to the ladder method for LSIP, which finds an optimal solution at a glp in the feasible region. For problems that do not have glp optimal solutions, we propose the addition of special artificial constraints to the constraint system of the problem to create a glp optimal solution. We present a ladder algorithm based on the maximum violation rule and an artificial ladder technique. Convergence results are provided with the support of some numerical tests.