一类变分不等式问题的信赖域算法  

Trust Region Algorithm for Solving a Class of Variational Inequality Problems

作　　者：欧宜贵[1] 侯定丕[2] 

机构地区：[1]海南大学数理系,海口570228 [2]中国科学技术大学数学系,合肥230026

出　　处：《应用数学》2002年第3期47-52,共6页Mathematica Applicata

摘　　要：基于J .M .Peng研究一类变分不等式问题 (简记为VIP)时所提出的价值函数 ,本文提出了求解强单调的VIP的一个新的信赖域算法 .和已有的处理VIP的信赖域方法不同的是 :它在每步迭代时 ,不必求解带信赖域界的子问题 ,仅解一线性方程组而求得试验步 .这样 ,计算的复杂性一般来说可降低 .在通常的假设条件下 ,文中还证明了算法的整体收敛性 .最后 ,在梯度是半光滑和约束是矩形域的假设下 ,该算法还是超线性收敛的 .Based on the merit function proposed by J.M.Peng for variational inequality problems (or VIP for short), we present a new trust region algorithm for VIP. Compared with those existing trust region methods for VIP, this method has a different feature: it obtains a step at each iteration not by solving a quadratic programming sub problem with a trust region bound, but by solving a system of linear equations. Thus it reduces computational complexity and improves computational efficiency. It is proven that this algorithm is globally convergent and the rate of convergence is superlinear under some conditions.

关 键 词：变分不等式 信赖域方法 整体收敛性 半光滑 超线性收敛 

分 类 号：O221[理学—运筹学与控制论]