一种无恢复过程的SQP-滤子法
|
摘要
本文研究非线性不等式约束优化问题,构造一个新的SQP-滤子法.该方法将滤子技术有机融合到简金宝提出的可行SQP方法中,利用转轴运算的思想,产生一个近似积极约束集,当QP子问题不相容时,利用广义投影技术获得可行搜索方向.该算法既能避免罚函数的选择,又能避免常规滤子算法中的恢复算法,一定程度上简化了计算.最后,在合理的条件下,证明了算法的全局收敛性.
In this paper, we consider the nonlinear inequality constrained optimization problem.A new SQP-filter method is presented. In the algorithm, the filter technique is combined to the feasible SQP method which is proposed by Jinbao Jian. An approximate active constraint set is produced by the idea of pivoting operation. When the QP subproblem is incompatible, the feasible direction of search is obtained by generalized gradient projection method. So this method is effective to avoid the restoration algorithm in general filter algorithm and the difficulties in choosing penalty parameter. Therefore, the computational cost is reduced. The theoretical analysis shows that the algorithm is global convergent under some suitable conditions.
In this paper, we consider the nonlinear inequality constrained optimization problem.A new SQP-filter method is presented. In the algorithm, the filter technique is combined to the feasible SQP method which is proposed by Jinbao Jian. An approximate active constraint set is produced by the idea of pivoting operation. When the QP subproblem is incompatible, the feasible direction of search is obtained by generalized gradient projection method. So this method is effective to avoid the restoration algorithm in general filter algorithm and the difficulties in choosing penalty parameter. Therefore, the computational cost is reduced. The theoretical analysis shows that the algorithm is global convergent under some suitable conditions.
引文
[1]简金宝.非线性最优化一个超线收敛的可行下降算法[J].数学杂志,1995(3):319-326.
[2] ZHOU G L. A modified SQP method and its global convergence[J]. Journal of Global Optimization,1997, 11(2):193-205.
[3] SHEN C G, ZHANG L H, WANG B, et al. Global and local convergence of a nonmonotone SQP method for constrained nonlinear optimization[J]. Computational Optimization and Applications,2014, 59(3):435-473.
[4] FLETCHER R, LEYFFER S. Nonlinear programming without a penalty function[J]. Ma-thematical Programming, 2002, 91(2):239-269.
[5] SHEN C G, XUE W J, PU D G. Global convergence of a tri-dimensional filter SQP algorithm based on the line search method[J]. Applied Numerical Mathematics, 2009, 59(2):235-250.
[6] SU K, CHE J R. A modified SQP-filter method and its global convergence[J]. Applied Mathematics and Computation, 2007, 194(1):92-101.
[7] WANG X L, ZHU Z B, ZUO S Y, et al. An SQP-filter method for inequality constrained optimization and its global convergence[J]. Applied Mathematics and Computational, 2011,217(24):10224-10230.
[8] JIAN J B, TANG C M. An SQP feasible descent algorithm for nonlinear inequality constrained optimization without strict complementarity[J]. Computers and Mathematics with Applications,2005,49(2):223-238.
[9] FLETCHER R, LEYFFER S, TOINT P. On the global convergence of a filter-SQP algorithm[J].SIAM J.Optim, 2002, 13(10):44-59.
[10]简金宝.光滑约束优化快速算法:理论分析与数值实验[M].北京:科学出版社,2010.
[2] ZHOU G L. A modified SQP method and its global convergence[J]. Journal of Global Optimization,1997, 11(2):193-205.
[3] SHEN C G, ZHANG L H, WANG B, et al. Global and local convergence of a nonmonotone SQP method for constrained nonlinear optimization[J]. Computational Optimization and Applications,2014, 59(3):435-473.
[4] FLETCHER R, LEYFFER S. Nonlinear programming without a penalty function[J]. Ma-thematical Programming, 2002, 91(2):239-269.
[5] SHEN C G, XUE W J, PU D G. Global convergence of a tri-dimensional filter SQP algorithm based on the line search method[J]. Applied Numerical Mathematics, 2009, 59(2):235-250.
[6] SU K, CHE J R. A modified SQP-filter method and its global convergence[J]. Applied Mathematics and Computation, 2007, 194(1):92-101.
[7] WANG X L, ZHU Z B, ZUO S Y, et al. An SQP-filter method for inequality constrained optimization and its global convergence[J]. Applied Mathematics and Computational, 2011,217(24):10224-10230.
[8] JIAN J B, TANG C M. An SQP feasible descent algorithm for nonlinear inequality constrained optimization without strict complementarity[J]. Computers and Mathematics with Applications,2005,49(2):223-238.
[9] FLETCHER R, LEYFFER S, TOINT P. On the global convergence of a filter-SQP algorithm[J].SIAM J.Optim, 2002, 13(10):44-59.
[10]简金宝.光滑约束优化快速算法:理论分析与数值实验[M].北京:科学出版社,2010.