非线性等式与有界约束优化问题的正割算法及其收敛性分析

Convergence of the Secant Algorithm for Nonlinear Equality and Box-Constrained Optimization

提出了结合仿射尺度技术的正割算法解非线性等式与有界约束优化问题.在合理假设下,证明了渐弱滤子线搜索方法可以保证新算法具有整体收敛性.通过引入一个高阶修正方向,克服Maratos效应的影响,使得算法二步q-超线性收敛于最优点.进一步地,对算法进行修改,使得新算法达到q-超线性收敛性.

The authors propose a new secant algorithm with the affine scaling technique for nonlinear equality and box-constrained optimization.The new algorithm with the line search dwindling filter method yields the global convergence under some reasonable conditions.A high-order modified direction is introduced in order to prevent the Maratos effect so that the algorithm converges locally two-step g-superlinearly.Furthermore,with some modifications,the convergence rate of the new approach is q-superlinear.