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DC Optimization Approach to Metric Regularity of Convex Multifunctions with Applications to Infinite Systems

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  • B. S. Mordukhovich

    (Wayne State University)

  • T. T. A. Nghia

    (Wayne State University)

Abstract

The paper develops a new approach to the study of metric regularity and related well-posedness properties of convex set-valued mappings between general Banach spaces by reducing them to unconstrained minimization problems with objectives given as the difference of convex (DC) functions. In this way, we establish new formulas for calculating the exact regularity bound of closed and convex multifunctions and apply them to deriving explicit conditions ensuring well-posedness of infinite convex systems described by inequality and equality constraints.

Suggested Citation

  • B. S. Mordukhovich & T. T. A. Nghia, 2012. "DC Optimization Approach to Metric Regularity of Convex Multifunctions with Applications to Infinite Systems," Journal of Optimization Theory and Applications, Springer, vol. 155(3), pages 762-784, December.
    • Handle: RePEc:spr:joptap:v:155:y:2012:i:3:d:10.1007_s10957-012-0092-8
    DOI: 10.1007/s10957-012-0092-8
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    References listed on IDEAS

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    1. M. Cánovas & M. López & B. Mordukhovich & J. Parra, 2012. "Quantitative stability of linear infinite inequality systems under block perturbations with applications to convex systems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 310-327, July.
    2. Stephen M. Robinson, 1976. "Regularity and Stability for Convex Multivalued Functions," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 130-143, May.
    3. Mirjam Dür, 2003. "A parametric characterization of local optimality," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 57(1), pages 101-109, April.
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    Cited by:

    1. Boris S. Mordukhovich & T. T. A. Nghia, 2014. "Nonsmooth Cone-Constrained Optimization with Applications to Semi-Infinite Programming," Mathematics of Operations Research, INFORMS, vol. 39(2), pages 301-324, May.

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