解等式约束规划的信赖域SQP滤子方法

讨论了一种信赖域SQP滤子方法的局部收敛性.滤子方法会遇到Maratos效应,尽管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上升,从而不被算法接受,于是破坏了算法的收敛性.给出一种修改后的信赖域SQP滤子算法,当完全步不被接受时,对算法进行二阶校正(SOC),可以减小其不可行性.修改后的算法可以避免Maratos效应,使算法达到局部超线性收敛.

Trust Region SQP Filter Method for Equality Constrained Optimization

The local convergence properties of the filter trust region algorithm was discussed. The filter approach can suffer from the so-called Maratos effect. Although the full Newton step may be a superlinear convergence step ,it increases both the objective function and the constrained violation if the iteration point is arbitrarily close to a strict local solution of the NLP,and is therefore rejected by the algorithm. In this case the Maratos effect occurs and results in poor local convergence behavior. As a remedy,the infeasibility is improved in this paper. A second order correction is used if the full step is rejected. It is shown that this modification is indeed able to prevent the Maratos effect so that the algorithm can obtain the local superlinear convergence.