求解一类广义随机线性互补问题的投影Levenberg-Marquardt方法  

Projected Levenberg-Marquardt Method for Solving a Class of Generalized Stochastic Linear Complementarity Problems

作　　者：王英晓 杜守强 

机构地区：[1]青岛大学数学与统计学院,青岛266071

出　　处：《上海工程技术大学学报》2017年第4期326-331,共6页Journal of Shanghai University of Engineering Science

基　　金：国家自然科学基金资助项目(11671220);山东省自然科学基金资助项目(ZR2016AM29)

摘　　要：首次提出一类含有有限个离散型随机变量的广义随机线性互补问题.基于FischerBurmeister函数,将问题转化为非光滑方程组,用投影Levenberg-Marquardt方法对转化的非光滑方程组进行求解.在一般条件下,证明了方法的全局收敛性,并且结合相关的数值实验,表明了方法的有效性.A class of generalized stochastic linear complementarity problems with finite discrete random variables was proposed for the first time.Based on Fischer-Burmeister function,the problem was transformed into nonsmooth equations,and a projected Levenberg-Marquardt method was used to solve this transformed nonsmooth equations.The global convergence properties of the proposed method were also proved under mild conditions,and the related numerical results illustrate that the method is efficient for solving generalized stochastic linear complementarity problems.

关 键 词：广义随机线性互补问题 FISCHER-BURMEISTER函数 投影Levenberg-Marquardt方法 

分 类 号：O221[理学—运筹学与控制论]