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An Approximate Exact Penalty in Constrained Vector Optimization on Metric Spaces

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  • A. J. Zaslavski

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Abstract

In this paper, we use the penalty approach in order to study a class of constrained vector minimization problems on complete metric spaces. A penalty function is said to have the generalized exact penalty property iff there is a penalty coefficient for which approximate solutions of the unconstrained penalized problem are close enough to approximate solutions of the corresponding constrained problem. For our class of problems, we establish the generalized exact penalty property and obtain an estimation of the exact penalty.

Suggested Citation

  • A. J. Zaslavski, 2014. "An Approximate Exact Penalty in Constrained Vector Optimization on Metric Spaces," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 649-664, August.
    • Handle: RePEc:spr:joptap:v:162:y:2014:i:2:d:10.1007_s10957-013-0288-6
    DOI: 10.1007/s10957-013-0288-6
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    References listed on IDEAS

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    1. Alexander J. Zaslavski, 2007. "Existence of Approximate Exact Penalty in Constrained Optimization," Mathematics of Operations Research, INFORMS, vol. 32(2), pages 484-495, May.
    2. Alexander J. Zaslavski, 2010. "Optimization on Metric and Normed Spaces," Springer Optimization and Its Applications, Springer, number 978-0-387-88621-3, June.
    3. R. S. Burachik & A. N. Iusem & J. G. Melo, 2010. "Duality and Exact Penalization for General Augmented Lagrangians," Journal of Optimization Theory and Applications, Springer, vol. 147(1), pages 125-140, October.
    4. X. X. Huang & X. Q. Yang, 2003. "A Unified Augmented Lagrangian Approach to Duality and Exact Penalization," Mathematics of Operations Research, INFORMS, vol. 28(3), pages 533-552, August.
    5. Willard I. Zangwill, 1967. "Non-Linear Programming Via Penalty Functions," Management Science, INFORMS, vol. 13(5), pages 344-358, January.
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    Cited by:

    1. Amos Uderzo, 2016. "A Strong Metric Subregularity Analysis of Nonsmooth Mappings Via Steepest Displacement Rate," Journal of Optimization Theory and Applications, Springer, vol. 171(2), pages 573-599, November.

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