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International Conference on Mathematics and Computing

ICMC 2017: Mathematics and Computing pp 232–245Cite as

A Davidon-Fletcher-Powell Type Quasi-Newton Method to Solve Fuzzy Optimization Problems

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Part of the book series: Communications in Computer and Information Science ((CCIS,volume 655))

Abstract

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.

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Acknowledgement

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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Authors and Affiliations

  1. Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi, Varanasi, 221005, Uttar Pradesh, India

    Debdas Ghosh

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  1. Debdas Ghosh
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Correspondence to Debdas Ghosh .

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Editors and Affiliations

  1. Haldia Institute of Technology, Haldia, India

    Debasis Giri

  2. University of Central Florida, Orlando, Florida, USA

    Ram N. Mohapatra

  3. Freie Universität Berlin, Berlin, Germany

    Heinrich Begehr

  4. Fordham University, Bronx, New York, USA

    Mohammad S. Obaidat

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Ghosh, D. (2017). A Davidon-Fletcher-Powell Type Quasi-Newton Method to Solve Fuzzy Optimization Problems. In: Giri, D., Mohapatra, R., Begehr, H., Obaidat, M. (eds) Mathematics and Computing. ICMC 2017. Communications in Computer and Information Science, vol 655. Springer, Singapore. https://doi.org/10.1007/978-981-10-4642-1_20

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  • DOI: https://doi.org/10.1007/978-981-10-4642-1_20

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-4641-4

  • Online ISBN: 978-981-10-4642-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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