Sun Min, Liu Jing
School of Management, Qufu Normal University, Shandong, 276826 P.R. China.
School of Mathematics and Statistics, Zaozhuang University, Shandong, 277160 P.R. China.
J Inequal Appl. 2017;2017(1):263. doi: 10.1186/s13660-017-1539-0. Epub 2017 Oct 23.
As a first-order method, the augmented Lagrangian method (ALM) is a benchmark solver for linearly constrained convex programming, and in practice some semi-definite proximal terms are often added to its primal variable's subproblem to make it more implementable. In this paper, we propose an accelerated PALM with indefinite proximal regularization (PALM-IPR) for convex programming with linear constraints, which generalizes the proximal terms from semi-definite to indefinite. Under mild assumptions, we establish the worst-case [Formula: see text] convergence rate of PALM-IPR in a non-ergodic sense. Finally, numerical results show that our new method is feasible and efficient for solving compressive sensing.
作为一种一阶方法，增广拉格朗日方法（ALM）是线性约束凸规划的基准求解器，并且在实际中，一些半定近端项经常被添加到其原始变量的子问题中以使其更易于实现。在本文中，我们针对线性约束凸规划提出了一种具有不定近端正则化的加速PALM（PALM-IPR），它将近端项从半定推广到不定。在温和假设下，我们建立了PALM-IPR在非遍历意义下的最坏情况[公式：见正文]收敛速率。最后，数值结果表明我们的新方法对于求解压缩感知是可行且有效的。
