约束优化一个结合积极集识别的强收敛模松弛SQP算法(英文)  

A Strongly Convergent Norm-relaxed SQP Algorithm with Active Set Identification for Constrained Optimization

作　　者：刘逸[1] 简金宝[2,3] 黄宗文[1] 

机构地区：[1]广西大学行健文理学院,南宁530004 [2]玉林师范学院数学与信息科学学院,玉林537000 [3]广西大学数学与信息科学学院,南宁530004

出　　处：《工程数学学报》2013年第1期145-158,共14页Chinese Journal of Engineering Mathematics

基　　金：The National Natural Science Foundation of China(11271086);he Natural Science Foundation of Guangxi Province(2011GXNSFD018022);he Innovation Group of Talents Highland of Guangxi Higher School

摘　　要：本文考虑了非线性不等式约束优化问题的求解问题,并结合模松弛SQP方法、强次可行方向法和积极集识别技术,提出了一个SQP算法.该算法在每一次迭代中,模松弛QP子问题的约束函数个数只决定于相应的识别集.不引进罚参数线搜索便可将阶段I(初始化)和阶段II(最优化)统一起来.在MFCQ条件下,得到算法的全局收敛性,若满足二阶充分条件,则算法具有强收敛性,且识别集能精确识别积极约束集.最后,我们给出了初步的数值结果.This paper deals with the solution of the optimization with nonlinear inequality constraint. Based on the norm-relaxed sequential quadratic programming （SQP） method and the method of strongly sub-feasible directions, an SQP algorithm with active set identification technique is proposed. At each iteration, the norm-relaxed quadratic programming subproblem only consists of the constraints corresponding to an active identification set. Without any penalty parameters, the line search tech- nique can help combine the initialization phase with the optimization phase. The global convergence is proved under the Mangasarian-Fromovitz constraint qualifica- tion. If the second order sufficient conditions are satisfied, the proposed algorithm is strongly convergent and the active constraints are exactly identified by the iden- tification sets. The preliminary numerical results are also reported.

关 键 词：约束优化 模松弛SQP方法 强次可行方向法 全局收敛和强收敛 积极识别集 

分 类 号：O221[理学—运筹学与控制论]