Solving generalized semi-infinite programs by reduction to simpler problems

The article intends to give a unifying treatment of different approaches to solve generalized semi-infinite programs by transformation to simpler problems. In particular dual-, penalty-, discretization-, reduction-, and Karush-Kuhn-Tucker (KKT)-methods are applied to obtain equivalent problems or relaxations of a simpler structure. The relaxations are viewed as a perturbation P-tau of the original problem P, depending on a perturbation parameter tau > 0, and are analyzed by using parametric programming techniques. We give convergence results and results on the rate of convergence for the minimal values and the optimal solutions of P-tau when tau tends toward 0. We review earlier studies and present new ones.