最小化三个凸函数之和的一个简单原始-对偶算法

摘要

提出一个简单的原始-对偶算法求解三个凸函数之和的最小化问题,其中目标函数包含有梯度李普希兹连续的光滑函数,非光滑函数和含有复合算子的非光滑函数.在新方法中,对偶变量迭代使用预估-矫正的方案.分析了算法的收敛性和收敛速率.最后,数值实验说明了算法的有效性.%In this study,we propose a simple primal-dual algorithm for minimization of a sum of three convex separable functions,which are involved a smooth function with Lipschitz continuous gradient,a nonsmooth function and a linear composite nonsmooth function.A predictor-corrector scheme to the dual variable is used in our algorithm.Convergence and convergence rate are also discussed.In the end,numerical results illustrate the efficiency of this method.