标题： 不可精确交替方向乘数方法用于可分离凸优化 显示英文标题

标题： Inexact alternating direction multiplier methods for separable convex optimization

摘要： 不精确的交替方向乘子方法（ADMMs）被用于解决具有线性约束的一般可分离凸优化问题，且目标函数是光滑项和非光滑项之和。 该方法涉及线性化子问题、回代步骤以及梯度或加速梯度技术。 建立了全局收敛性。 当ADMM子问题没有闭式解或子问题的解成本较高时，这些方法特别有用。 基于图像重建问题的数值实验表明了所提出方法的有效性。 显示英文摘要

摘要： Inexact alternating direction multiplier methods (ADMMs) are developed for solving general separable convex optimization problems with a linear constraint and with an objective that is the sum of smooth and nonsmooth terms. The approach involves linearized subproblems, a back substitution step, and either gradient or accelerated gradient techniques. Global convergence is established. The methods are particularly useful when the ADMM subproblems do not have closed form solution or when the solution of the subproblems is expensive. Numerical experiments based on image reconstruction problems show the effectiveness of the proposed methods.