Cubic Interpolation: A Line Search Technique for Fuzzy Optimization Problems

Abstract

This article continues the research on line search techniques for fuzzy optimization problems. Previously, in Ghosh and Chakraborty (Int J Appl Comput Math 3(2):527–547, 2017), a quadratic interpolation technique for fuzzy optimization problem was studied. In this article, we propose a cubic interpolation technique. For the optimality concept, a partial ordering of fuzzy numbers is used. In order to derive the cubic interpolation method, the generalized Hukuhara difference between a pair of fuzzy numbers and the generalized Hukuhara differentiability for fuzzy functions are applied. The convergence analysis of the proposed technique is also exhibited. It is found that the developed method has quadratic rate of convergence. A detailed numerical example is included to explore the developed technique. The iteration points in the example are also pictorially shown in detail. © 2017, Springer (India) Private Ltd., part of Springer Nature.