A Davidon-Fletcher-Powell Type Quasi-Newton Method to Solve Fuzzy Optimization Problems
In this article, a Davidon-Fletcher-Powell type quasi-Newton method is proposed to capture nondominated solutions of fuzzy optimization problems. The functions that we attempt to optimize here are multivariable fuzzy-number-valued functions. The decision variables are considered to be crisp. Towards developing the quasi-Newton method, the notion of generalized Hukuhara difference between fuzzy numbers, and hence generalized Hukuhara differentiability for multi-variable fuzzy-number-valued functions are used. In order to generate the iterative points, the proposed technique produces a sequence of positive definite inverse Hessian approximations. The convergence result and an algorithm of the developed method are also included. It is found that the sequence in the proposed method has superlinear convergence rate. To illustrate the developed technique, a numerical example is exhibited.
KeywordsQuasi-Newton method Generalized-Hukuhara differentiability Fuzzy optimization Nondominated solution
The author is truly thankful to the anonymous reviewers and editors for their valuable comments and suggestions. The financial support through Early Career Research Award (ECR/2015/000467), Science and Engineering Research Board, Government of India is also gratefully acknowledged.
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