Xiaoling Fu – Optimization Online

On the Iteration Complexity of Some Projection Methods for Monotone Linear Variational Inequalities

Published: 2015/01/13

Complementarity and Variational Inequalities convergence rate, iteration complexity, linear variational inequality, projection methods

Projection type methods are among the most important methods for solving monotone linear variational inequalities. In this note, we analyze the iteration complexity for two projection methods and accordingly establish their worst-case O(1/t) convergence rates measured by the iteration complexity in both the ergodic and nonergodic senses, where t is the iteration counter. Our analysis … Read more

Block-wise Alternating Direction Method of Multipliers with Gaussian Back Substitution for Multiple-block Convex Programming

Published: 2014/09/16

Convex Optimization alternating direction method of multipliers, big data, centralized computing, convergence rate, convex optimization, distributed computing, splitting methods

We consider the linearly constrained convex minimization model with a separable objective function which is the sum of m functions without coupled variables, and discuss how to design an efficient algorithm based on the fundamental technique of splitting the augmented Lagrangian method (ALM). Our focus is the specific big-data scenario where m is huge. A … Read more