Ming-Jun Lai – Optimization Online

Parallel Multi-Block ADMM with o(1/k) Convergence

Published: 2014/03/18

Constrained Nonlinear Optimization, Convex Optimization admm, alternating direction method of multipliers, convergence rate, parallel and distributed computing

This paper introduces a parallel and distributed extension to the alternating direction method of multipliers (ADMM). The algorithm decomposes the original problem into N smaller subproblems and solves them in parallel at each iteration. This Jacobian-type algorithm is well suited for distributed computing and is particularly attractive for solving certain large-scale problems. This paper introduces … Read more

Augmented L1 and Nuclear-Norm Models with a Globally Linearly Convergent Algorithm

Published: 2012/01/22, Updated: 2013/03/09

Ming-Jun Lai

Wotao Yin

Nonsmooth Optimization compressed sensing, global linear convergence, low rank matrix, matrix recovery, sparse optimization

This paper studies the long-existing idea of adding a nice smooth function to “smooth” a non-differentiable objective function in the context of sparse optimization, in particular, the minimization of $||x||_1+1/(2\alpha)||x||_2^2$, where $x$ is a vector, as well as those of the minimization of $||X||_*+1/(2\alpha)||X||_F^2$, where $X$ is a matrix and $||X||_*$ and $||X||_F$ are the … Read more