局部超线性收敛的信赖域SQP滤子方法

讨论信赖域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.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,影响了算法的收敛速度.对R.Fletcher,S.Leyffer和L.Toint在"SQP滤子全局收敛算法(2002)"文中的算法进行了修改,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),使得它容易被滤子接受,保证算法具有局部超线性收敛性.

Local Convergence of Trust Region Filter SQP Method

The local convergence properties of the filter trust region algorithm are 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, a full Newton step increases both the objective function and the constraint violation, and is therefore rejected by the falter, even though it could be a very good step toward the solution. This can result in poor local convergence behavior. As a remedy, if the full Newton step is rejected, by means of a seconde order correction which aims to further reduce infeasibility. This modification is indeed able to prevent the Maratos effect.