求解不等式约束优化问题无严格互补松弛条件的QP-Free新算法  

A New QP-Free Algorithm for Inequality Constrained Optimization without Strict Complementarity

作　　者：王永丽[1] 韩丛英[2] 李田[1] 李明强[1] 

机构地区：[1]山东科技大学信息科学与工程学院,青岛266590 [2]中国科学院大学科技资源管理研究中心,北京100049

出　　处：《应用数学学报》2013年第1期1-13,共13页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(10971122;11101420);山东省自然科学基金(Y2008A01);山东省博士基金(2010BSE06047);高等学校博士点专项科研基金(20093718110005)资助项目

摘　　要：本文针对不等式约束优化问题,结合Facchinei-Fischer-Kanzow精确有效集识别技术,给出一个新的线性方程组与辅助方向相结合的可行下降算法.算法每步迭代只需求解一个降维的线性方程组或计算一次辅助方向,且获取辅助方向的投影矩阵只涉及近似有效约束集中的元素,问题规模大为减少,且当迭代次数充分大时,只需求解一个降维的线性方程组.无需严格互补松弛条件,算法全局且一步超线性收敛.In this paper, based on the Facchinei-Fischer-Kanzow active set identification technique, a new QP-Free Mgorithm is proposed for solving inequality constrained optimiza- tion problem. At each iteration, an auxiliary direction or a system of linear equations is computed to obtain a search direction. When the iteration is sufficiently large, only a sys- tem of linear equations is solved. In particular, the auxiliary direction is obtained by using a reduced matrix, the scale of which is much smaller than that of the Generalized Projec- tion Gradient matrix. Without strict complementarity, the new algorithm is proved to be globally convergent with a superlinear convergence rate under assumptions milder than the strong second order sufficient condition.

关 键 词：不等式约束优化 SQP算法 QP-Free算法 广义投影梯度 全局收敛性 超线性收敛性 

分 类 号：O221.2[理学—运筹学与控制论]