Convergence Rate of a Simulated Annealing Algorithm with Noisy Observations

In this paper we propose a modified version of the simulated annealing algorithm for solving a stochastic global optimization problem. More precisely, we address the problem of finding a global minimizer of a function with noisy evaluations. We provide a rate of convergence and its optimized parametrization to ensure a minimal number of evaluations for a given accuracy and a confidence level close to 1. This work is completed with a set of numerical experimentations and assesses the practical performance both on benchmark test cases and on real world examples.