学术
摘 要:
讨论了信赖域SQP滤子方法的局部收敛性。SQP滤子方法是解非线性规划的一种较为有效的方法，但是滤子方法也会遇到Maratos效应。虽然完全牛顿步可能是一个超线性收敛步，但是当迭代点充分靠近原问题的严格局部解时，完全牛顿步可能会使目标函数值和约束违反度都上升，从而不被滤子接受，于是就影响了算法的收敛速度。对FLETCHERR，LEYFFERS，Ph．TOINTL在On the global convergence of a filter-SQP algorithm（2002）一文中的信赖域SQP滤子方法进行了修改，提出了一类新的算法：在这类算法中，如果完全牛顿步不被滤子接受，就通过对它进行一个二阶校正（SOC）来使得它容易被接受。[著者文摘]
文章出处:
《上海第二工业大学学报》-2007年24卷4期 -306-316页
分 类 号:
文献标识码:
A
文章编号:
1001-4543（2007）04-0306-11
Trust Region Filter SQP Method for Nonlinear Programming： Local Convergence
WANG Hua, GUISheng-hua （1. Departmant of Mathematics, Tongji University, Shanghai, 200092, ER.China; 2. Shanghai Second Polytechnic University, Shanghai 201209, ER.China）
Abstract:
In this paper the local convergence properties of the filter trust region algorithm is discussed. The filter approach can suffer from the so-called Maratos effect. The Maratos effect occurs if, arbitrarily close to a strict local solution of the NLP（1 ）-（2）, a full Newton step increases both the objective function and the constraint violation, and is therefore rejected by the filter, even though it could be a very good step toward the solution. This can result in poor local convergence behavior. As a remedy, we propose in this paper that if the full Newton step is rejected, by means of a second order correction which aims to further reduce infeasibility. We also show that this modification is indeed able to prevent the Maratos effect.[著者文摘]
Key words:
SQPmethod; trust region; filter; second order correction; Maratoseffect; local convergence
基金资助:
国家自然科学基金资助项目（No.10571137）;上海教委科研项目（No.05RZ12）
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