一类修正正割方法解非线性约束优化问题的超线性收敛性(英文)

Superlinear convergence of improved secant methods for nonlinear constrained optimization

提出了一类解非线性等式约束优化问题的修正正割方法.通过应用二阶校正技术改进搜索方向,修正由Fotecilla提出的产生二步超线性收敛的正割方法.证明了在合理的假设条件下该算法具有一步超线性收敛性.数据结果表明了本算法的有效性.

We propose a class of improved secant methods for nonlinear equality constrained optimization based on adding second order correction steps. The new methods differ from the original secant methods introduced by Fontecilla that generate a sequence converging two-step q-superlinearly. Under mild assumptions it is shown that the new algorithms can improve the search direction so that the local one-step superlinear convergence is achieved. The numerical results indicate that the improved algorithms are effective.