An Exact Algorithm Based on the Kuhn–Tucker Conditions for Solving Linear Generalized Semi‐Infinite Programming Problems

Abstract

Optimization problems containing a finite number of variables and an infinite number of constraints are called semi‐infinite programming problems. Under certain conditions, a class of these problems can be represented as bi‐level programming problems. Bi‐level problems are a particular class of optimization problems, in which there is another optimization problem embedded in one of the constraints. We reformulate a semi‐infinite problem into a bi‐level problem and then into a single‐level nonlinear one by using the Kuhn–Tucker optimality conditions. The resulting reformulation allows us to employ a branch and bound scheme to optimally solve the problem. Computational experimentation over well‐known instances shows the effectiveness of the developed method concluding that it is able to effectively solve linear semi‐infinite programming problems. Additionally, some linear bi‐level problems from literature are used to validate the robustness of the proposed algorithm.