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A Lower Bound for the Penalty Parameter in the Exact Minimax Penalty Function Method for Solving Nondifferentiable Extremum Problems

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  • T. Antczak

    (University of Łódź)

Abstract

In the paper, we consider the exact minimax penalty function method used for solving a general nondifferentiable extremum problem with both inequality and equality constraints. We analyze the relationship between an optimal solution in the given constrained extremum problem and a minimizer in its associated penalized optimization problem with the exact minimax penalty function under the assumption of convexity of the functions constituting the considered optimization problem (with the exception of those equality constraint functions for which the associated Lagrange multipliers are negative—these functions should be assumed to be concave). The lower bound of the penalty parameter is given such that, for every value of the penalty parameter above the threshold, the equivalence holds between the set of optimal solutions in the given extremum problem and the set of minimizers in its associated penalized optimization problem with the exact minimax penalty function.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:159:y:2013:i:2:d:10.1007_s10957-013-0335-3
    DOI: 10.1007/s10957-013-0335-3
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    References listed on IDEAS

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    1. Tadeusz Antczak, 2010. "THEl1PENALTY FUNCTION METHOD FOR NONCONVEX DIFFERENTIABLE OPTIMIZATION PROBLEMS WITH INEQUALITY CONSTRAINTS," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 27(05), pages 559-576.
    2. Willard I. Zangwill, 1967. "Non-Linear Programming Via Penalty Functions," Management Science, INFORMS, vol. 13(5), pages 344-358, January.
    3. Antczak, Tadeusz, 2009. "Exact penalty functions method for mathematical programming problems involving invex functions," European Journal of Operational Research, Elsevier, vol. 198(1), pages 29-36, October.
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    Cited by:

    1. Tadeusz Antczak & Najeeb Abdulaleem, 2021. "E-differentiable minimax programming under E-convexity," Annals of Operations Research, Springer, vol. 300(1), pages 1-22, May.
    2. 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.

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