proximal gradient algorithm – Optimization Online

A general double-proximal gradient algorithm for d.c. programming

Published: 2016/10/20

Nonsmooth Optimization convergence analysis, d.c. programming, kurdyka--\l ojasiewicz property, proximal gradient algorithm, toland dual

The possibilities of exploiting the special structure of d.c. programs, which consist of optimizing the difference of convex functions, are currently more or less limited to variants of the DCA proposed by Pham Dinh Tao and Le Thi Hoai An in 1997. These assume that either the convex or the concave part, or both, are … Read more

The proximal-proximal gradient algorithm

Published: 2013/05/05, Updated: 2013/08/27

Ting Kei Pong

Applications - Science and Engineering, Convex and Nonsmooth Optimization, Nonlinear Optimization alternating direction method, alternating direction method of multipliers, iteration complexity, proximal gradient algorithm, proximal mapping

We consider the problem of minimizing a convex objective which is the sum of a smooth part, with Lipschitz continuous gradient, and a nonsmooth part. Inspired by various applications, we focus on the case when the nonsmooth part is a composition of a proper closed convex function P and a nonzero affine map, with the … Read more