Methods for finding global optimal solutions to linear programs with equilibrium constraints. (Q696138)

By using the Kuhn-Tucker theorem on optimality conditions, the authors reformulate a linear programming problem with equilibrium constraints as an ordinary linear problem with a complementary constraint. To solve this latter problem they propose two branch-and-bound algorithms that are frequently used in global optimization. The first algorithm is based on simplicial subdivision and the second one on a binary tree. Both of these algirithms produce an \(\epsilon\)-global optimal solution for any given positive \(\epsilon.\) Preliminary computational experiences are also provided.