有界约束半光滑方程组的非单调投影信赖域方法  

A non-monotone projected trust-region method for bound-constrained semismooth equations

作　　者：孙冬梅[1] 朱德通[1] 

机构地区：[1]上海师范大学数理学院,上海200234

出　　处：《高校应用数学学报（A辑）》2009年第4期425-434,共10页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(10471094);教育部博士点基金(0527003);上海市重点学科(T0401);上海市教委基金(05DZ11)

摘　　要：投影信赖域策略结合非单调线搜索算法解有界约束非线性半光滑方程组。基于简单有界约束的非线性优化问题构建信赖域子问题,半光滑类牛顿步在可行域投影得到投影牛顿的试探步,获得新的搜索方向,结合非单调线搜索技术得到回代步,获得新的步长。在合理的条件下,证明算法不仅具有整体收敛性且保持超线性收敛速率。引入非单调技术能克服高度非线性的病态问题,加速收敛性进程,得到超线性收敛速率。In this paper, a projected trust-region algorithm with non-monotone line search technique is developed and analyzed for solving bound-constrained semismooth systems of equations. Based on a simply constrained differentiable minimization reformulation, a search direction by computing trial steps is obtained with a semismooth Newton-like method that is augmented by a projection onto the feasible set. Using search direction combining with line search, the quadratic model at each iteration generates backtracking step to obtain a new accepted step. The global convergence and local superlinear convergence rate of the proposed algorithm are established under some reasonable conditions. The nonmonotouic criterion is used to speed up the convergence progress in the contours of objective function with large curvature.

关 键 词：投影信赖域方法 非单调线搜索技术 有界约束 半光滑方程组 全局收敛性 局部超线性收敛 

分 类 号：O221.2[理学—运筹学与控制论]