非光滑优化算法的研究

Algorithm for nonsmooth optimization

探讨一种求解非光滑优化特殊问题——分片光滑问题的算法.在分析了非光滑优化两类基本算法以及最速下降法要素的基础上,提出了一种求解非光滑优化问题的思路,形成了算法.给出了算法的步骤及几种实现方式,对算法与次梯度法和光滑最速下降法的关系做了说明;最后,通过应用举例对所提出来的算法进行验证,将算法与其他几种经典算法进行了比较.

A new method is obtained for a special nondifferentiable problem--piecewise smooth optimization. After observing two types of nonsmooth optimization methods, subgradient method and Bundle method,and the descent method briefly, a new idea on solving nondifferentiable problems is brought forward and then the new method is presented. At the end, an important numerical experience is made to show the achievement of the new method. With the results, the new algorithm is compared with several classical algorithms.