A Quasi-Newton Method for Solving Fuzzy Optimization Problems

In this paper, we develop a quasi-Newton method for unconstrained optimization problems with fuzzy functions. Here, we extend the well-know BFGS method to fuzzy optimization problems. To this end, the generalized Hukuhara differentiability for fuzzy functions is employed. By using a Hessian approximation, we resolve the high computational cost of finding the Hessian in Newton method for fuzzy optimization problems. Utilizing the quasi-Newton algorithm, we find nondominated solutions of a fuzzy optimization problem. Finally, we provide some numerical examples to show the efficiency of the proposed approach over the other methods

fuzzy optimization problem, quasi-Newton method, generalized Hukuhara differentiability, nondominated solution