In this paper, we introduce TITAN, a novel inerTIal block majorizaTion minimizAtioN framework for non-smooth non-convex optimization problems. To the best of our knowledge, TITAN is the first framework of block-coordinate update method that relies on the majorization-minimization framework while embedding inertial force to each step of the block updates. The inertial force is obtained via an extrapolation operator that subsumes heavy-ball and Nesterov-type accelerations for block proximal gradient methods as special cases. By choosing various surrogate functions, such as proximal, Lipschitz gradient, Bregman, quadratic, and composite surrogate functions, and by varying the extrapolation operator, TITAN produces a rich set of inertial block-coordinate update methods. We study sub-sequential convergence as well as global convergence for the generated sequence of TITAN. We illustrate the effectiveness of TITAN on two important machine learning problems, namely sparse non-negative matrix factorization and matrix completion.

翻译：在本文中,我们引入了TITAN, 这是用于非摩擦非convex优化问题的新颖的InerTIal 块状主要IATION 缩微米izAtioN 框架。 据我们所知, TITAN是块状协调更新方法的第一个框架,它依赖主要-最小化框架,同时将惯性力量嵌入区块更新的每个步骤。 惯性力量是通过一个外推操作器获得的,该外推操作器将块状精度梯度方法的重球和Nesterov型加速作为特例。 我们通过选择各种代孕功能,如proximal、Lipschitz梯度、Bregman、四边形和复合替代功能,以及不同的外推操作器, TITAN产生一套丰富的惯性惯性区块协调更新方法。 我们研究了产生TITAN序列的次顺序趋同以及全球趋同。 我们说明了TITAN在两个重要的机器学习问题上的有效性, 即零度非内基质矩阵化和矩阵完成。