A GENERAL STOCHASTIC OUTER APPROXIMATIONS METHOD

Optimization problems involving an infinite number of constraints are considered. This paper presents a general stochastic outer approximati ons method which incorporates mechanisms for active search of relevant constraints and for dropping of irrelevant constraints. The method ex tracts the characteristic features of several stochastic outer approxi mations algorithms suggested by Wardi [J. Optim. Theory Appl., 56 (198 8), pp. 285-311; J. Optim. Theory Appl., 64 (1990), pp. 615-640] and f urthermore develops the approach to get advantages of the Eaves-Zangwi ll scheme. Similarly to Gonzaga and Polak [SIAM J. Control Optim., 17 (1979), pp. 477-493] the method is based on the use of quasi-optimalit y functions satisfying some general unrestricted assumptions. These fu nctions are usually employed in the stopping criteria of numerical tec hniques for solving simpler problems. It is shown that the method's tr ajectories almost surely converge to the quasioptimal set. Following t he proposed approach a stochastic algorithm for solving the approximat ion problem is constructed and studied. The proposed general method ca n be considered as a developed Eaves-Zangwill method applying the mult istart technique at each iteration for the search of relevant constrai nts' parameters.