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
相关论文
共 50 条
  • [21] A Smoothing Newton Method with Fischer-Burmeister Function for Second-Order Cone Complementarity Problems
    Narushima, Yasushi
    Sagara, Nobuko
    Ogasawara, Hideho
    [J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2011, 149 (01) : 79 - 101
  • [22] A smoothing quasi-Newton method for solving general second-order cone complementarity problems
    Tang, Jingyong
    Zhou, Jinchuan
    [J]. JOURNAL OF GLOBAL OPTIMIZATION, 2021, 80 (02) : 415 - 438
  • [23] A Smoothing Newton Method with Fischer-Burmeister Function for Second-Order Cone Complementarity Problems
    Yasushi Narushima
    Nobuko Sagara
    Hideho Ogasawara
    [J]. Journal of Optimization Theory and Applications, 2011, 149 : 79 - 101
  • [24] A smoothing quasi-Newton method for solving general second-order cone complementarity problems
    Jingyong Tang
    Jinchuan Zhou
    [J]. Journal of Global Optimization, 2021, 80 : 415 - 438
  • [25] A new one-step smoothing Newton method for the second-order cone complementarity problem
    Fang, Liang
    Han, Congying
    [J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2011, 34 (03) : 347 - 359
  • [26] A Combined Newton Method for Second-Order Cone Programming
    Chi, Xiaoni
    Peng, Jin
    [J]. SIXTH INTERNATIONAL SYMPOSIUM ON NEURAL NETWORKS (ISNN 2009), 2009, 56 : 605 - 612
  • [27] Smoothing Newton algorithm for the second-order cone programming with a nonmonotone line search
    Jingyong Tang
    Li Dong
    Liang Fang
    Jinchuan Zhou
    [J]. Optimization Letters, 2014, 8 : 1753 - 1771
  • [28] Smoothing Newton algorithm for the second-order cone programming with a nonmonotone line search
    Tang, Jingyong
    Dong, Li
    Fang, Liang
    Zhou, Jinchuan
    [J]. OPTIMIZATION LETTERS, 2014, 8 (05) : 1753 - 1771
  • [29] A smoothing Newton algorithm for solving the monotone second-order cone complementarity problems
    College of Mathematics and Information Science, Xinyang Normal University, Xinyang 464000, China
    不详
    不详
    [J]. J. Appl. Math. Comp., 2012, 1-2 (45-61): : 45 - 61
  • [30] Smoothing Newton method for nonsmooth second-order cone complementarity problems with application to electric power markets
    Chen, Pin-Bo
    Lin, Gui-Hua
    Zhu, Xide
    Bai, Fusheng
    [J]. JOURNAL OF GLOBAL OPTIMIZATION, 2021, 80 (03) : 635 - 659
12345