# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1907.02368