MSS: MATLAB Software for L-BFGS Trust-Region Subproblems for Large-Scale Optimization

TL;DR

This paper introduces MSS, a MATLAB software implementing an L-BFGS trust-region subproblem solver that improves efficiency in large-scale optimization by reducing function and gradient evaluations.

Contribution

It adapts the More-Sorensen method to an L-BFGS setting with a stable direct solver, enabling accurate solutions for large-scale problems.

Findings

Requires fewer function and gradient evaluations than Steihaug-Toint method

Provides solutions to any user-defined accuracy in large-scale optimization

Demonstrates effectiveness on CUTEr benchmark problems

Abstract

A MATLAB implementation of the More-Sorensen sequential (MSS) method is presented. The MSS method computes the minimizer of a quadratic function defined by a limited-memory BFGS matrix subject to a two-norm trust-region constraint. This solver is an adaptation of the More-Sorensen direct method into an L-BFGS setting for large-scale optimization. The MSS method makes use of a recently proposed stable fast direct method for solving large shifted BFGS systems of equations [13, 12] and is able to compute solutions to any user-defined accuracy. This MATLAB implementation is a matrix-free iterative method for large-scale optimization. Numerical experiments on the CUTEr [3, 16]) suggest that using the MSS method as a trust-region subproblem solver can require significantly fewer function and gradient evaluations needed by a trust-region method as compared with the Steihaug-Toint method.