Solving semi-infinite programs by smoothing projected gradient method (Q480937)

A semi-infinite programming (SIP) problem with a convex set constraint is considered. Using the value function of the lower level problem, the SIP problem is reformulated as a nonsmooth optimization problem. By Dankin's theorem the value function is Lipschitz continuous and its Clarke generalized gradients can be computed. By using the nonsmooth Karush-Kuhn-Tucker conditions, stationary conditions are defined under suitable constraint qualifications. The authors present a new numerical method for solving the problem which uses the integral entropy function to approximate the value function and then solve the SIP problem by the smoothing projected gradient method. Under suitable conditions, the iteration sequence converges to a stationary point of the problem. The authors study the error bounds between the integral entropy function and the value function and between locally optimal solutions of the smoothing problem and those for the original problem. Some estimates for locally optimal solutions of the problem are derived under some second-order sufficient conditions. Numerical results show that the algorithm is efficient for solving the SIP problem.