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A Quasi-Newton Method with Rank-Two Update to Solve Interval Optimization Problems

  • Debdas GhoshEmail author
Original Paper

Abstract

In this study, a quasi-Newton method is developed to obtain efficient solutions of interval optimization problems. The idea of generalized Hukuhara differentiability for multi-variable interval-valued functions is employed to derive the quasi-Newton method. Through an inverse-Hessian approximation with rank-two modification, the proposed technique sidesteps the high computational cost for the computation of inverse-Hessian in Newton method for interval optimization problems. The rank-two modification of inverse-Hessian approximation is applied to generate the iterative points in the quasi-Newton technique. A sequential algorithm and the convergence result of the derived method are also presented. 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.

Keywords

Interval optimization Quasi-Newton method Generalized-Hukuhara differentiability Efficient solution 

Mathematics Subject Classification

90C30 65K05 

Notes

Acknowledgments

The author is thankful to three anonymous reviewers and editors for their valuable comments and suggestions. The author gratefully acknowledges the financial support through Early Career Research Award (ECR/2015/000467), Science & Engineering Research Board, Government of India.

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Copyright information

© Springer India Pvt. Ltd. 2016

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Information Technology KalyaniKalyaniIndia

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