An optimal subgradient algorithm for large-scale bound-constrained convex optimization

TL;DR

This paper introduces an efficient implementation of the OSGA algorithm for large-scale bound-constrained convex optimization, demonstrating its effectiveness through numerical experiments in signal processing, machine learning, and statistics.

Contribution

It develops an explicit and inexact scheme for solving the bound-constrained subproblem within OSGA, enabling efficient large-scale problem solving.

Findings

OSGA achieves optimal complexity for bound-constrained problems

Numerical experiments show promising performance on large-scale applications

Software implementation of OSGA is available for practical use

Abstract

This paper shows that the OSGA algorithm -- which uses first-order information to solve convex optimization problems with optimal complexity -- can be used to efficiently solve arbitrary bound-constrained convex optimization problems. This is done by constructing an explicit method as well as an inexact scheme for solving the bound-constrained rational subproblem required by OSGA. This leads to an efficient implementation of OSGA on large-scale problems in applications arising signal and image processing, machine learning and statistics. Numerical experiments demonstrate the promising performance of OSGA on such problems. ions to show the efficiency of the proposed scheme. A software package implementing OSGA for bound-constrained convex problems is available.