A Quadratic Fuzzy Penalty Method for Solving a Class of Nonlinear Fuzzy Optimization Problems

Some important methods for solving constrained fuzzy optimization problems replace the original problem by a sequence of sub-problems in which the constraints are represented by terms added to the objective function. In this paper, we describe one approach of this type for solving a class of nonlinear fuzzy optimization problems. The fuzzy quadratic penalty method adds a multiple of the square of the violation of each constraint to the objective function. The penalty terms for the constraint violations are multiplied by a positive coefficient. By making this coefficient larger, we penalize constraint violations more severely, thereby forcing the minimizer of the penalty function closer to the feasible region for the constrained problem. We described the quadratic fuzzy penalty method and investigate convergence of this method.