关于Lemaréchal高阶算法的研究——概念性算法

Study on Lemaréchal's High Order Algorithm: Conceptual Algorithm

中文摘要:

      对于非光滑的极小化问题,C.Lemaréchel在[1]中对凸函数的无约束极小化问题提示了一个高阶σ-牛顿型算法的思想,并讨论了某些性质。本文对[1]的高阶σ-牛顿型算法作了进一步研究,并提出一个概念性算法,证明了算法的全局收敛性。

英文摘要:

      C.Lemaréchal proposed an idea of high order σ-Newton type algorithm for nonsmooth convex functions in ( 1 ).some properties were discussed there.In this paper, we study more about this high order σ-Newton type algo-rithm, and give a conceptual algorithm.The grobal convergence has been proved.