A smoothing Newton method for mathematical programs governed by second-order cone constrained generalized equations

被引：11
|
作者：
Wu, Jia [1 ]
Zhang, Liwei [1 ]
Zhang, Yi [1 ]
机构：
[1] Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China
来源：
JOURNAL OF GLOBAL OPTIMIZATION | 2013年 / 55卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Smoothing Newton method; Generalized equations; Second-order cone; MPEC; Optimality conditions; LINEAR COMPLEMENTARITY CONSTRAINTS; EQUILIBRIUM CONSTRAINTS; CONVERGENCE PROPERTIES; OPTIMIZATION PROBLEMS; NONLINEAR PROGRAMS; RELAXATION SCHEME; SQP METHODS; REGULARIZATION; PENALIZATION; ALGORITHM;
D O I：
10.1007/s10898-012-9880-9
中图分类号：
C93 [管理学]; O22 [运筹学];
学科分类号：
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要：
In this paper, we consider a class of mathematical programs governed by second-order cone constrained parameterized generalized equations. We reformulate the necessary optimality conditions as a system of nonsmooth equations under linear independence constraint qualification and the strict complementarity condition. A set of second order sufficient conditions is proposed, which is proved to be sufficient for the second order growth of the stationary point. The smoothing Newton method in [40] is employed to solve the system of nonsmooth equations whose strongly BD-regularity at a solution point is demonstrated under the second order sufficient conditions. Several illustrative examples are provided and discussed.
引用
收藏
页码：359 / 385
页数：27
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