THE MINIMAX EXACT PENALTY FUZZY FUNCTION METHOD FOR SOLVING CONVEX NONSMOOTH OPTIMIZATION PROBLEMS WITH FUZZY OBJECTIVE FUNCTIONS

. Optimization problems under uncertainty has achieved much attention because of inaccurate or incomplete data that often appear in realworld applications. In order to address this challenging issue, several types of methodologies have been developed in optimization theory and one of them is fuzzy optimization. In this paper, an attempt is taken to use the minimax exact penalty function method for solving convex nondifferentiable optimization problems with fuzzy objective functions and with both inequality and equality constraints. The most important property of exact penalty function methods, that is, exactness of the penalization, is defined and analyzed if the minimax penalty function method is applicable for solving a convex nondifferentiable optimization problem with a fuzzy objective function. It is proved that a (weak) KKT point of the considered fuzzy optimization problem is a (weakly) nondominated solution of its associated fuzzy penalized optimization problem constructed in the used penalized approach. Further, the conditions are also derived under which there is the equivalence between (weakly) nondominated solutions of the aforesaid fuzzy optimization problems. These results are established under assumption that the functions involved in the considered nondifferentiable fuzzy optimization problem are convex. Further, the algorithm of solving the considered nondifferentiable fuzzy optimization problem by using the minimax exact penalty fuzzy function method is proposed and its convergence is also established.