Cubic Interpolation: A Line Search Technique for Fuzzy Optimization Problems

Cubic Interpolation: A Line Search Technique for Fuzzy Optimization Problems 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Applied and Computational Mathematics Springer Journals

Cubic Interpolation: A Line Search Technique for Fuzzy Optimization Problems

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Publisher
Springer India
Copyright
Copyright © 2017 by Springer (India) Private Ltd., part of Springer Nature
Subject
Mathematics; Applications of Mathematics; Mathematical Modeling and Industrial Mathematics; Operations Research/Decision Theory; Theoretical, Mathematical and Computational Physics; Computational Science and Engineering; Nuclear Energy
ISSN
2349-5103
eISSN
2199-5796
D.O.I.
10.1007/s40819-017-0450-1
Publisher site
See Article on Publisher Site

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.

Journal

International Journal of Applied and Computational MathematicsSpringer Journals

Published: Dec 2, 2017

References

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