A cyclic block coordinate descent method with generalized gradient projections

TL;DR

This paper introduces a convergence analysis for a broad class of gradient projection methods using non-Euclidean metrics and Armijo linesearch, applicable to smooth, constrained, possibly nonconvex optimization problems.

Contribution

It develops a general framework for block-coordinate descent methods with gradient projections employing non-Euclidean metrics and linesearch, extending existing convergence results.

Findings

Convergence is established for the proposed class of methods.

The framework accommodates nonconvex and separable constraints.

The methods improve flexibility in constrained optimization algorithms.

Abstract

The aim of this paper is to present the convergence analysis of a very general class of gradient projection methods for smooth, constrained, possibly nonconvex, optimization. The key features of these methods are the Armijo linesearch along a suitable descent direction and the non Euclidean metric employed to compute the gradient projection. We develop a very general framework from the point of view of block--coordinate descent methods, which are useful when the constraints are separable.