Simulated Annealing for Convex Optimization: Rigorous Complexity Analysis and Practical Perspectives

Riley Badenbroek () and Etienne Klerk ()
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Riley Badenbroek: Erasmus University Rotterdam
Etienne Klerk: Tilburg University

Journal of Optimization Theory and Applications, 2022, vol. 194, issue 2, No 4, 465-491

Abstract: Abstract We give a rigorous complexity analysis of the simulated annealing algorithm by Kalai and Vempala (Math Oper Res 31(2):253–266, 2006) using the type of temperature update suggested by Abernethy and Hazan (International Conference on Machine Learning, 2016). 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.

Keywords: Simulated annealing; Convex optimization; Hit-and-run sampling; Semidefinite and copositive programming; 90C25; 90C59 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10957-022-02034-x

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