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Calmness and Exact Penalization in Constrained Scalar Set-Valued Optimization

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  • X. X. Huang

    (Chongqing University)

Abstract

In this paper, we study a class of constrained scalar set-valued optimization problems, which includes scalar optimization problems with cone constraints as special cases. We introduce (local) calmness of order α for this class of constrained scalar set-valued optimization problems. We show that the (local) calmness of order α is equivalent to the existence of a (local) exact set-valued penalty map.

Suggested Citation

  • X. X. Huang, 2012. "Calmness and Exact Penalization in Constrained Scalar Set-Valued Optimization," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 108-119, July.
    • Handle: RePEc:spr:joptap:v:154:y:2012:i:1:d:10.1007_s10957-012-9998-4
    DOI: 10.1007/s10957-012-9998-4
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    References listed on IDEAS

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    1. X. M. Yang & D. Li & S. Y. Wang, 2001. "Near-Subconvexlikeness in Vector Optimization with Set-Valued Functions," Journal of Optimization Theory and Applications, Springer, vol. 110(2), pages 413-427, August.
    2. A. Moldovan & L. Pellegrini, 2009. "On Regularity for Constrained Extremum Problems. Part 1: Sufficient Optimality Conditions," Journal of Optimization Theory and Applications, Springer, vol. 142(1), pages 147-163, July.
    3. X. X. Huang & X. Q. Yang & K. L. Teo, 2007. "Lower-Order Penalization Approach to Nonlinear Semidefinite Programming," Journal of Optimization Theory and Applications, Springer, vol. 132(1), pages 1-20, January.
    4. Giovanni Crespi & Ivan Ginchev & Matteo Rocca, 2006. "First-order optimality conditions in set-valued optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(1), pages 87-106, February.
    5. 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.
    6. A. Moldovan & L. Pellegrini, 2009. "On Regularity for Constrained Extremum Problems. Part 2: Necessary Optimality Conditions," Journal of Optimization Theory and Applications, Springer, vol. 142(1), pages 165-183, July.
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    Cited by:

    1. X. Huang, 2013. "Convergence of a class of penalty methods for constrained scalar set-valued optimization," Journal of Global Optimization, Springer, vol. 56(4), pages 1501-1513, August.

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