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Nonsmooth Interval-Valued Optimization and Saddle-Point Optimality Criteria

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Abstract

In this article, we focus our attention on a nonsmooth interval-valued optimization problem and establish sufficient optimality conditions for a feasible solution to be an LU optimal solution under the invexity assumption. Appropriate duality theorems for Wolfe and Mond–Weir-type duals are presented in order to relate the LU optimal solution of primal and dual programs. Moreover, saddle-point-type optimality conditions are established in order to find relation between LU optimal solution of primal and saddle point of Lagrangian function.

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Acknowledgments

The research of the first author was partially supported by DST, New Delhi, India, through Grant no. SR/FTP/MS-007/2011. The authors wish to thank the referees for their valuable suggestions which improved the presentation of the paper.

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Authors and Affiliations

  1. Department of Applied Mathematics, Indian School of Mines, Dhanbad, Jharkhand, 826 004, India

    Anurag Jayswal & Jonaki Banerjee

  2. Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    I. Ahmad

Authors
  1. Anurag Jayswal
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  2. I. Ahmad
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  3. Jonaki Banerjee
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Correspondence to Anurag Jayswal.

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Communicated by Anton Abdulbasah Kamil.

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Jayswal, A., Ahmad, I. & Banerjee, J. Nonsmooth Interval-Valued Optimization and Saddle-Point Optimality Criteria. Bull. Malays. Math. Sci. Soc. 39, 1391–1411 (2016). https://doi.org/10.1007/s40840-015-0237-7

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  • DOI: https://doi.org/10.1007/s40840-015-0237-7

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