【摘要】 交替极小化方法是求解变量分块凸优化问题的一个基本的方法,其主要困难在于有效地求解交替极小化过程中产生的两个子问题.在本文中,通过借助近似线性化技术,我们设计了两个交替极小化方法的变体.第一个变体适合于两个子问题之一容易求解而另一个不容易求解的情形;第二个变体则适合并行计算.理论上,基于近似算子的相关知识,我们首先将交替极小化变体进行了形式上的统一,然后在恰当的假设条件下证明了算法的次线性收敛性.更多还原

【Abstract】 The alternating minimization( AM) method is a fundamental method for minimizing convex functions whose variables consist of two blocks. How to efficiently solve each subproblem when applying the AM method is the most concerned task. In this paper we investigate this task and design two new variants of the AM method by borrowing proximal linearized techniques. The first variant is suitable for the case where one of the subproblems is hard to solve and the other can be directly computed. The second variant is designed for parallel computation. Theoretically,with the help of proximal operators,we first formulate the AM variants into a unified form,and then show sublinear convergence results under some mild assumptions.更多还原