An infeasible bundle method for nonconvex constrained optimization with application to semi-infinite programming problems

The main difficulty for solving semi-infinite programming (SIP) problem is precisely that it has infinitely many constraints. By using a maximum function, the SIP problem can be rewritten as a nonconvex nonsmooth constrained optimization (NNCO) problem. Global convergence in most of constrained optimization algorithms has traditionally been enforced by the use of a penalty function or filter strategy. In this paper, we propose an infeasible bundle method for NNCO problem based on the so-called improvement functions, without a penalty function and filter strategy. The method appears to be more direct and easier to implement, in the sense that it is closer in spirit and structure to the well-developed unconstrained bundle methods. Under a special constraint qualification, the sequence generated by this algorithm converges to the KKT point of the NNCO problem as well as the SIP problems. Preliminary numerical results show that this algorithm is robust and efficient for NNCO problems and SIP problems.