随机增广Lagrange变分不等式的一种求解方法
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摘要
利用变分不等式求解优化问题是一种有效且便利的方法.而随机变分不等式和增广Lagrange变分不等式的概念最近以一种新的形式被阐述,在凸性条件下求解这类问题通常用的方法是逐步对冲算法和分解算法.对于随机优化问题,提出随机增广Lagrange变分不等式.在凸凹鞍点问题中,由随机分解算法求解这类问题.
Variational inequality was an effective and convenient method for solving optimization problems. The concept of a stochastic variational inequality and augmented Lagrange variational inequality has recently been elaborated in a new form. The usual methods for solving these problems were progressive hedging and decomposition algorithms. For stochastic optimization problems,stochastic augmented variational inequalities were proposed. In convex and concave saddle point problems,stochastic decomposition algorithm was used to solve these problems.
Variational inequality was an effective and convenient method for solving optimization problems. The concept of a stochastic variational inequality and augmented Lagrange variational inequality has recently been elaborated in a new form. The usual methods for solving these problems were progressive hedging and decomposition algorithms. For stochastic optimization problems,stochastic augmented variational inequalities were proposed. In convex and concave saddle point problems,stochastic decomposition algorithm was used to solve these problems.
引文
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[5]CHEN X,FUKUSHIMA M. Expected residual minimization method for stochastic linear complementary problems[J]. Math Oper Res,2005,30(4):1022-1038.
[6]CHEN X,ZHANG C,FUKUSHIMA M. Robust solution of monotone stochastic linear complementarity problems[J]. Math Program,2009,117(1-2):51-80.
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[9]ROCKAFELLAR R T. Progressive decoupling of linkages in monotone variational inequalities and convex optimization[J]. Set-Valued and Variational Analysis,2018:1-31.
[10]ROCKAFELLAR R T,SUN J. Solving monotone stochastic variational inequalities and complementarity problems by progressive hedging[J].Math Program,2018:1-19.
[11]王炜,李伟梅,李忠伟.基于BE-散度的不确定投资组合优化问题的等价形式[J].辽宁师范大学学报(自然科学版),2018,41(4):433-438.
[12]王炜,李伟梅,何淼,等.基于JS-散度的不确定概率约束优化方法[J].吉林师范大学学报(自然科学版),2018,39(2):54-58.
[2]STEPHEN M,ROBINSON. Generalized equations and their solutions,partⅡ:Applications to nonlinear programming[M]. Berlin Heidelberg:Springer,1982.
[3]ROCKAFELLAR R T,WETS J B. Stochastic variational inequalities:single-stage to multistage[J]. Math Program,2016,165(1):1-30.
[4]FACCHINEI F,PANG J S. Finite-dimensional variational inequalities and complementarity problems[M]. Switzerland:Springer,2003.
[5]CHEN X,FUKUSHIMA M. Expected residual minimization method for stochastic linear complementary problems[J]. Math Oper Res,2005,30(4):1022-1038.
[6]CHEN X,ZHANG C,FUKUSHIMA M. Robust solution of monotone stochastic linear complementarity problems[J]. Math Program,2009,117(1-2):51-80.
[7]GRKAN G,ZGE A Y,ROBINSON S M. Sample-path solution of stochastic variational inequalities[J]. Math Program,1999,84(2):313-333.
[8]IUSEM A N,JOFRE A,OLIVEIRA R I,et al. Extragradient method with variance reduction for stochastic variational inequalities[J]. Siam J Optimiz,2017,27(2):1-39.
[9]ROCKAFELLAR R T. Progressive decoupling of linkages in monotone variational inequalities and convex optimization[J]. Set-Valued and Variational Analysis,2018:1-31.
[10]ROCKAFELLAR R T,SUN J. Solving monotone stochastic variational inequalities and complementarity problems by progressive hedging[J].Math Program,2018:1-19.
[11]王炜,李伟梅,李忠伟.基于BE-散度的不确定投资组合优化问题的等价形式[J].辽宁师范大学学报(自然科学版),2018,41(4):433-438.
[12]王炜,李伟梅,何淼,等.基于JS-散度的不确定概率约束优化方法[J].吉林师范大学学报(自然科学版),2018,39(2):54-58.