线性均衡约束最优化的一个广义投影强次可行方向法  

A Generalized Projection Strongly Subfeasible Directions Method for Optimization with Linear Complementarity Constraints

作　　者：梁玉梅[1] 简金宝[2] 覃义[3] 

机构地区：[1]上海大学数学系,上海200444 [2]广西大学数学与信息科学学院,广西南宁530004 [3]桂林电子工业学院数学系,广西桂林541004

出　　处：《运筹学学报》2005年第3期56-64,共9页Operations Research Transactions

基　　金：国家自然科学基金(No.10261001)广西科学基金(No.0236001;0249003)

摘　　要：本文讨论带线性均衡约束最优化问题,首先利用摄动技术和一个互补函数将问题等价转化为一般约束最优化问题,然后结合广义投影技术和强次可行方向法思想,建立了问题的一个新算法.算法在迭代过程中保证搜索方向不为零,从而使得每次迭代只需计算一次广义投影.在适当的条件下,证明了算法的全局收敛性,并对算法进行了初步的数值试验.This paper discusses a special class of mathematical programs with linear complementarity constraints. We first reformulate the discussed problem as a general constrained optimization problems by means of perturbed technique and a generalized smoothing complementarity function. Then, a new algorithm is presented by making use of the generalized projection technique and the idea of strongly subfeasible directions method. The algorithm needs to compute only one generalized projection at each iteration. Global convergence of this algorithm is established under appropriate assumptions. Some preliminary computational results are reported.

关 键 词：运筹学 均衡约束 最优化 约束最优化问题 强次可行方向法 广义投影 线性均衡 迭代过程 全局收敛性 等价转化 摄动技术 投影技术 

分 类 号：O224[理学—运筹学与控制论] O221.2[理学—数学]