minimization algorithm – Optimization Online

A primal-dual splitting algorithm for finding zeros of sums of maximally monotone operators

Published: 2012/06/26

Convex Optimization duality, maximally monotone operator, minimization algorithm, operator splitting, resolvent, subdifferential

We consider the primal problem of finding the zeros of the sum of a maximally monotone operator with the composition of another maximally monotone operator with a linear continuous operator and a corresponding dual problem formulated by means of the inverse operators. A primal-dual splitting algorithm which simultaneously solves the two problems in finite-dimensional spaces … Read more

A Monotone+Skew Splitting Model for Composite Monotone Inclusions in Duality

Published: 2010/11/27

Luis M. Briceno-Arias

Patrick L. Combettes

Convex Optimization, Nonsmooth Optimization composite operator, convex optimization, decomposition, duality, fenchel-rockafellar duality, minimization algorithm, monotone inclusion, monotone operator, operator splitting

The principle underlying this paper is the basic observation that the problem of simultaneously solving a large class of composite monotone inclusions and their duals can be reduced to that of finding a zero of the sum of a maximally monotone operator and a linear skew-adjoint operator. An algorithmic framework is developed for solving this … Read more