Random projections for trust region subproblems

TL;DR

This paper explores the use of random projections to efficiently approximate solutions to trust region subproblems, which are central to derivative-free optimization methods.

Contribution

It introduces a novel approach applying random projections to solve trust region subproblems approximately, enhancing computational efficiency.

Findings

Random projections can effectively approximate trust region subproblems.

The method reduces computational complexity in derivative-free optimization.

Preliminary results show promising accuracy and efficiency improvements.

Abstract

The trust region method is an algorithm traditionally used in the field of derivative free optimization. The method works by iteratively constructing surrogate models (often linear or quadratic functions) to approximate the true objective function inside some neighborhood of a current iterate. The neighborhood is called "trust region in the sense that the model is trusted to be good enough inside the neighborhood. Updated points are found by solving the corresponding trust region subproblems. In this paper, we describe an application of random projections to solving trust region subproblems approximately.