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

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.