A SMOOTHING SCHEME FOR OPTIMIZATION PROBLEMS WITH MAX-MIN CONSTRAINTS

(Communicated by Adil Bagirov) Abstract. In this paper, we apply a smoothing approach to a minimization problem with a max-min constraint (i.e., a min-max-min problem). More specifically, we first rewrite the min-max-min problem as an optimization prob-lem with several min-constraints and then approximate each min-constraint function by a smooth function. As a result, the original min-max-min opti-mization problem can be solved by solving a sequence of smooth optimization problems. We investigate the relationship between the global optimal value and optimal solutions of the original min-max-min optimization problem and that of the approximate smooth problem. Under some conditions, we show that the limit points of the first-order (second-order) stationary points of the smooth optimization problems are first-order (second-order) stationary points of the original min-max-min optimization problem. 1. Introduction. Conside