Non-Convex Optimization by Hamiltonian Alternation

TL;DR

This paper presents a new metaheuristic method for non-convex optimization that uses Hamiltonian alternation to escape local minima, demonstrated on spin glass ground state problems.

Contribution

Introduces a novel Hamiltonian alternation technique that improves non-convex optimization by escaping local minima, applicable even without known ground state energy.

Findings

Effective in escaping local minima in non-convex problems

Improves finding ground states in spin glass models

Works with or without known ground state energy

Abstract

A major obstacle to non-convex optimization is the problem of getting stuck in local minima. We introduce a novel metaheuristic to handle this issue, creating an alternate Hamiltonian that shares minima with the original Hamiltonian only within a chosen energy range. We find that repeatedly minimizing each Hamiltonian in sequence allows an algorithm to escape local minima. This technique is particularly straightforward when the ground state energy is known, and one obtains an improvement even without this knowledge. We demonstrate this technique by using it to find the ground state for instances of a Sherrington-Kirkpatrick spin glass.