Mathematical Programs with Semidefinite Cone Complementarity Constraints: Constraint Qualifications and Optimality Conditions

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Indexed by:期刊论文

Date of Publication:2014-03-01

Journal:SET-VALUED AND VARIATIONAL ANALYSIS

Included Journals:SCIE、Scopus

Document Type:J

Volume:22

Issue:1

Page Number:155-187

ISSN No.:1877-0533

Key Words:Mathematical program with semidefinite cone complementarity; constraints; B-stationary condition; Constraint qualifications; Second-order sufficient conditions

Abstract:The tangent cone of gph plays an important role in developing necessary conditions for mathematical programs with semidefinite cone complementarity constraints. We demonstrate an elegant formula for the tangent cone of gph, based on which the Bouligand stationary point is characterized explicitly. The relationships among different stationary points under certain constraint qualifications are discussed. Then we propose a second order sufficient condition which can be weakened under the strict complementarity condition. Importantly, for the sake of algorithm design, under the assumption of strict complementarity condition, we give a nonsmooth equation reformulation of the stationary point, whose smoothing system is verified to be nonsingular at the stationary point under the proposed second order sufficient condition.