A quasi-Newton method with rank-two update to solve fuzzy optimization problems

Abstract

In this article, we develop a quasi-Newton method to obtain nondominated solutions of fuzzy optimization problems. The objective function of the optimization problem under consideration is a fuzzy-number-valued function. The notion of generalized Hukuhara difference of fuzzy numbers, and hence generalized Hukuhara differentiability for multi-variable fuzzy-number-valued functions are used to develop the quasi-Newton method. The proposed technique produces a sequence of positive definite inverse Hessian approximations to generate the iterative points. A sequential algorithm and the convergence result of the proposed method are also given. It is obtained that the sequence in the proposed method has superlinear convergence rate. The method is also found to have quadratic termination property. Two numerical examples are provided to illustrate the developed technique. © 2017, Sociedad Española de Matemática Aplicada.