一个解非光滑凸规划的整体收敛性算法

A Global Convergence Method for Nondifferentiable Convex Programing

本文根据文献次梯度聚集原理,构造一个求解问题min max x∈k N1<i<nf_i(x)的新算法。其中f_i:R^N→R^1是局部Lipschitz凸函数(不一定可微,i=1,2,…,n)。此方法简化了[5]的方法。同时提出了一种基于Armijo策略的线性搜索方法,在目标函数有下界的假设下证明了算法的整体收敛性。

According to the theorem of aggregate subgradient in K. C. Kiwiel and C. Lemarechal, we set up a new mothod for the problem (1.1). The method needs only the value and subgradient of objebtive function at the test point. The search direction can be found by solving a quadratic programing. This method simplified the method in, and the global convergence of the method has been proved under the condition of the objective function bounded from below.