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

B. S. Mordukhovich () and T. T. A. Nghia
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B. S. Mordukhovich: Wayne State University
T. T. A. Nghia: Wayne State University

Journal of Optimization Theory and Applications, 2012, vol. 155, issue 3, No 2, 762-784

Abstract: 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.

Keywords: Variational analysis; Optimization; Convex multifunctions; Metric regularity (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10957-012-0092-8

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