relative error – Optimization Online

A relative-error inertial-relaxed inexact projective splitting algorithm

Published: 2020/02/18

Convex and Nonsmooth Optimization inertial algorithms, monotone operators, operator splitting, projective splitting, relative error

For solving structured monotone inclusion problems involving the sum of finitely many maximal monotone operators, we propose and study a relative-error inertial-relaxed inexact projective splitting algorithm. The proposed algorithm benefits from a combination of inertial and relaxation effects, which are both controlled by parameters within a certain range. We propose sufficient conditions on these parameters … Read more

Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward-backward splitting, and regularized Gauss-Seidel methods

Published: 2010/12/22

Hédy Attouch

Jérôme Bolte

Benar Fux Svaiter

Nonlinear Optimization alternating direction method, block-coordinate methods, descent methods, forward-backward splitting, iterative thresholding, kurdyka-lojasiewicz inequality, nonconvex nonsmooth optimization, o-minimal structures, proximal algorithms, relative error, semi-algebraic optimization, sufficient decrease, tame optimization

In view of the minimization of a nonsmooth nonconvex function f, we prove an abstract convergence result for descent methods satisfying a sufficient-decrease assumption, and allowing a relative error tolerance. Our result guarantees the convergence of bounded sequences, under the assumption that the function f satisfies the Kurdyka-Lojasiewicz inequality. This assumption allows to cover a … Read more