一个解可分凸优化问题的部分预校正分裂法

考虑线性约束的可分离凸优化问题,其目标函数可分为没有耦合变量的3个独立的凸函数.基于扩展的轮换方向乘子法,提出了一个新的解可分离凸优化问题的部分预校正分裂法,此算法在校正步中考虑对第1个变量不进行校正,对第2个和第3个变量进行校正;并且在较弱的条件下,证明了此算法的收敛性.

A Partial Prediction correction Splitting Method for Solving Separable Convex Optimization Problems

By considering the separable convex optimization problems with linear constraints, their objective function can be divided into three independent convex functions without coupling variables. Based on the extension of alternating direction of multipliers, this paper presents a new partial prediction correction splitting method for solving separable convex optimization problems, this algorithm considers that the first variable is not corrected in correction step but the second variable and third variable are corrected. In addition, the convergence of this algorithm is proved under weaker condition.