Composite Self-Concordant Minimization

TL;DR

This paper introduces a variable metric optimization framework for minimizing composite functions involving self-concordant and non-smooth convex components, with proven convergence and novel step-size strategies, demonstrated through applications and experiments.

Contribution

It presents a new variable metric method for composite self-concordant minimization with convergence guarantees and innovative step-size procedures.

Findings

Convergence is established without Lipschitz gradient assumptions.

The framework is applicable to various real-world problems.

Numerical experiments validate the effectiveness of the proposed methods.

Abstract

We propose a variable metric framework for minimizing the sum of a self-concordant function and a possibly non-smooth convex function, endowed with an easily computable proximal operator. We theoretically establish the convergence of our framework without relying on the usual Lipschitz gradient assumption on the smooth part. An important highlight of our work is a new set of analytic step-size selection and correction procedures based on the structure of the problem. We describe concrete algorithmic instances of our framework for several interesting applications and demonstrate them numerically on both synthetic and real data.