Equivalent Conditions for Jacobian Nonsingularity in Linear Symmetric Cone Programming

Lingchen Kong (), Levent Tunçel () and Naihua Xiu ()
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Lingchen Kong: Beijing Jiaotong University
Levent Tunçel: University of Waterloo
Naihua Xiu: Beijing Jiaotong University

Journal of Optimization Theory and Applications, 2011, vol. 148, issue 2, No 8, 364-389

Abstract: Abstract In this paper we consider the linear symmetric cone programming (SCP). At a Karush-Kuhn-Tucker (KKT) point of SCP, we present the important conditions equivalent to the nonsingularity of Clarke’s generalized Jacobian of the KKT nonsmooth system, such as primal and dual constraint nondegeneracy, the strong regularity, and the nonsingularity of the B-subdifferential of the KKT system. This affirmatively answers an open question by Chan and Sun (SIAM J. Optim. 19:370–396, 2008).

Keywords: Linear symmetric cone programming; Nonsingularity; Constraint nondegeneracy; Strong regularity; Variational analysis (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s10957-010-9758-2

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