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

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.