本文对非线性规划问题给出了一个具有一步超线性收敛速度的可行方法,由于此算法每步迭代均在可行域内进行,并且每步迭代只需计算一个二次子规划和一个逆矩阵,因而算法具有较好的实用价值,本文还在较弱的条件下证明了算法的全局收敛和一步超线性收敛性.
Abstract
In this paper, a one-step superlinearly convergent feasible algorithm for non-linear programming with nonlinear onstraints is proposed. Since the point generated by the algorithm is feasilbe per iteration and the algorithm only needs solve a sub-quadratic programming and a inverse matrix, the new algorithm has some good properties for tractical use. Under some milder conditions, the global convergence and local superlinear convergence are proven in this paper.
关键词
约束优化 /
SQP方法 /
可行方法 /
收敛性
{{custom_keyword}} /
Key words
Constrained optimization /
SQP method /
feasible method /
convergence
{{custom_keyword}} /
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1] E.R.Panier and A.L.Tits.A Superlinear Convergence Feasible Method for the Solution of in Equality Constrained Optimization Problems,SIAM J.Control and Optimization,1987,25 (4):934-950.
[2] A.L.Tits,W.T.Nye and.4.5.Vincentell.Enhanced Methods of Feasible Directions for Engineering Design Problems,JOTA,1986,51 (3):475-504.
[3] M.J.D.Powell.The Convergence of Variable Metric Methods for Nonlinearly Constrained Optimization Calculations,Nonlinear Prog.3,D.L.Mangasarian et.al.,eds,New York:Academic Press,1973,
[4] 27-63.
[5] E.Polak,R.Trahan and D.(a.Mayne.Combined Phase-I-Phase-II Methods of Feasible Directions,Math.Prog.,1979,17:32-61.
[6] 韩继业等.非线性规划讲义,北京:中国科学院应用数学研究所印,1983.
[7] 堵丁柱.非线性约束条件下的梯度投影方法,应用数学学报,1985,8 (1):7-16.
[8] 高自友.一类求解非线性约束下的可行方向法,高杖应用数学学报,1990,4:457-476.
[9] J.F.A.De,O.Pantoja and D.Q.Mayne.Exact penalty function algorithm with simple updating of the penalty parameter,JOTA,1991,69 (1):441-467.
[10] J.Herskovits.A Two-Stage Feasible Directions Algorithm for Nonlinear Constrained Optimization,Math.Prog.,1986,36:19-38.
[11] 高自友,贺国平.约束条件下的广义梯度投影方法,科学通报,1991,19:1444-1447.
[12] Gao Ziyou.Feasible Mecthods for Nonlinear Programming with Nonlinear Constraints and Their Convergent Properties,Ph.D.Thesis,Institute of Applied Mathematics,Academia Sinica,Beijing,1993.
[13] M.Fukushima.A Successive Cauadratic Programming Algorithm with Global and Superlinear Convergence Properties,Math.Prog.,1986,35:253-264.
{{custom_fnGroup.title_cn}}
脚注
{{custom_fn.content}}
基金
国家自然科学基金
{{custom_fund}}
PDF(652 KB)
