Properties of equation reformulation of the Karush-Kuhn-Tucker condition for nonlinear second order cone optimization problems

Indexed by:期刊论文

Journal:MATHEMATICAL METHODS OF OPERATIONS RESEARCH

Included Journals:EI、SCIE、Scopus

Volume:70

Issue:2

Page Number:195-218

ISSN No.:1432-2994

Key Words:Second order cone; Equation reformulation; Constraint nondegeneracy condition; Strong second order sufficient condition; SQP-type method

Abstract:We give an equation reformulation of the Karush-Kuhn-Tucker (KKT) condition for the second order cone optimization problem. The equation is strongly semismooth and its Clarke subdifferential at the KKT point is proved to be nonsingular under the constraint nondegeneracy condition and a strong second order sufficient optimality condition. This property is used in an implicit function theorem of semismooth functions to analyze the convergence properties of a local sequential quadratic programming type (for short, SQP-type) method by Kato and Fukushima (Optim Lett 1:129-144, 2007). Moreover, we prove that, a local solution x* to the second order cone optimization problem is a strict minimizer of the Han penalty merit function when the constraint nondegeneracy condition and the strong second order optimality condition are satisfied at x*.

Date of Publication:2009-10-01