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论文类型：期刊论文
发表时间：2010-04-01
发表刊物：SCIENCE CHINA-MATHEMATICS
收录刊物：SCIE
卷号：53
期号：4
页面范围：1025-1038
ISSN号：1674-7283
关键字：second-order cone programming problem; smoothing metric projector; B-subdifferential; Clarke's generalized Jacobian; smoothing Newton method
摘要：Based on the differential properties of the smoothing metric projector onto the second-order cone, we prove that, for a locally optimal solution to a nonlinear second-order cone programming problem, the nonsingularity of the Clarke's generalized Jacobian of the smoothing Karush-Kuhn-Tucker system, constructed by the smoothing metric projector, is equivalent to the strong second-order sufficient condition and constraint nondegeneracy, which is in turn equivalent to the strong regularity of the Karush-Kuhn-Tucker point. Moreover, this nonsingularity property guarantees the quadratic convergence of the corresponding smoothing Newton method for solving a Karush-Kuhn-Tucker point. Interestingly, the analysis does not need the strict complementarity condition.