fenchel-rockafellar duality – Optimization Online

A primal-dual splitting method for convex optimization involving Lipschitzian, proximable and linear composite terms

Published: 2011/12/16

Convex and Nonsmooth Optimization convex and nonsmooth optimization, douglas-rachford method, fenchel-rockafellar duality, forward-backward method, monotone inclusion, monotone operator, operator splitting, primal-dual algorithms, proximal method, saddle point problem

We propose a new first-order splitting algorithm for solving jointly the primal and dual formulations of large-scale convex minimization problems involving the sum of a smooth function with Lipschitzian gradient, a nonsmooth proximable function, and linear composite functions. This is a full splitting approach in the sense that the gradient and the linear operators involved … 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