Simulated annealing with hit-and-run for convex optimization: rigorous complexity analysis and practical perspectives for copositive programming

TL;DR

This paper provides a rigorous polynomial-time complexity analysis of a simulated annealing algorithm for convex optimization, introduces practical modifications, and demonstrates its effectiveness on copositive programming problems.

Contribution

It offers the first rigorous complexity analysis of the algorithm with practical improvements and numerical validation for copositive programming.

Findings

Algorithm runs in polynomial time with high probability

Practical modifications improve performance

Numerical results validate effectiveness on test problems

Abstract

We give a rigorous complexity analysis of the simulated annealing algorithm by Kalai and Vempala [Math of OR 31.2 (2006): 253-266] using the type of temperature update suggested by Abernethy and Hazan [arXiv 1507.02528v2, 2015]. The algorithm only assumes a membership oracle of the feasible set, and we prove that it returns a solution in polynomial time which is near-optimal with high probability. Moreover, we propose a number of modifications to improve the practical performance of this method, and present some numerical results for test problems from copositive programming.