root-finding – Optimization Online

Level-set methods for convex optimization

Published: 2016/02/23

Convex Optimization gauges, level sets, newton and secant methods, root-finding, sparse and low-rank recovery

Convex optimization problems arising in applications often have favorable objective functions and complicated constraints, thereby precluding first-order methods from being immediately applicable. We describe an approach that exchanges the roles of the objective and constraint functions, and instead approximately solves a sequence of parametric level-set problems. A zero-finding procedure, based on inexact function evaluations and … Read more

Sparse optimization with least-squares constraints

Published: 2010/02/09

Michael P. Friedlander

Ewout van den Berg

Applications - Science and Engineering, Nonsmooth Optimization basis pursuit, compressed sensing, convex optimization, duality, group sparsity, matrix completion, root-finding, sparse solutions

The use of convex optimization for the recovery of sparse signals from incomplete or compressed data is now common practice. Motivated by the success of basis pursuit in recovering sparse vectors, new formulations have been proposed that take advantage of different types of sparsity. In this paper we propose an efficient algorithm for solving a … Read more