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An Exact Minimax Penalty Function Method and Saddle Point Criteria for Nonsmooth Convex Vector Optimization Problems

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  • Anurag Jayswal

    (Indian School of Mines)

  • Sarita Choudhury

    (Indian School of Mines)

Abstract

In this paper, the exact minimax penalty function method is applied to solve constrained multiobjective optimization problems involving locally Lipschitz functions. The criteria for a saddle point for the original vector optimization problem are studied with the help of the penalized unconstrained vector optimization problem. Furthermore, we determine the conditions for which the (weak) efficient solutions of the vector optimization problem are equivalent to those of the associated, penalized unconstrained vector optimization problem. Some examples of nonsmooth multiobjective problems solved by using the exact minimax penalty method are presented to illustrate the results established in the paper.

Suggested Citation

  • Anurag Jayswal & Sarita Choudhury, 2016. "An Exact Minimax Penalty Function Method and Saddle Point Criteria for Nonsmooth Convex Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 169(1), pages 179-199, April.
    • Handle: RePEc:spr:joptap:v:169:y:2016:i:1:d:10.1007_s10957-015-0812-y
    DOI: 10.1007/s10957-015-0812-y
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    References listed on IDEAS

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    1. M. K. Ghosh & A. J. Shaiju, 2004. "Existence of Value and Saddle Point in Infinite-Dimensional Differential Games," Journal of Optimization Theory and Applications, Springer, vol. 121(2), pages 301-325, May.
    2. T. Antczak, 2013. "A Lower Bound for the Penalty Parameter in the Exact Minimax Penalty Function Method for Solving Nondifferentiable Extremum Problems," Journal of Optimization Theory and Applications, Springer, vol. 159(2), pages 437-453, November.
    3. G. Di Pillo & S. Lucidi & F. Rinaldi, 2012. "An approach to constrained global optimization based on exact penalty functions," Journal of Global Optimization, Springer, vol. 54(2), pages 251-260, October.
    4. S. Lucidi & F. Rinaldi, 2010. "Exact Penalty Functions for Nonlinear Integer Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 145(3), pages 479-488, June.
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