moreau envelope – Page 2 – Optimization Online

A variable smoothing algorithm for solving convex optimization problems

Published: 2012/07/13

Applications - Science and Engineering, Convex Optimization, Data-Mining fast gradient method, moreau envelope, regularization, variable smoothing

In this article we propose a method for solving unconstrained optimization problems with convex and Lipschitz continuous objective functions. By making use of the Moreau envelopes of the functions occurring in the objective, we smooth the latter to a convex and differentiable function with Lipschitz continuous gradient by using both variable and constant smoothing parameters. … Read more

Joint minimization with alternating Bregman proximity operators

Published: 2004/12/28

Heinz Bauschke

Patrick L. Combettes

Dominikus Noll

Convex Optimization alternating direction method, alternating projection methods, bregman distance, bregman projection, left proximity operator, moreau envelope, prox operator, proximal point algorithm, right proximity operator

A systematic study of the proximity properties of Bregman distances is carried out. This investigation leads to the introduction of a new type of proximity operator which complements the usual Bregman proximity operator. We establish key properties of these operators and utilize them to devise a new alternating procedure for solving a broad class of … Read more