Article Dans Une Revue EURO Journal on Computational Optimization Année : 2025

Direct-search methods in the year 2025: Theoretical guarantees and algorithmic paradigms

Résumé

Optimizing a function without using derivatives is a challenging paradigm, that precludes from using classical algorithms from nonlinear optimization, and may thus seem intractable other than by using heuristics. Nevertheless, the field of derivative-free optimization has succeeded in producing algorithms that do not rely on derivatives and yet are endowed with convergence guarantees. One class of such methods, called direct-search methods, is particularly popular thanks to its simplicity of implementation, even though its theoretical underpinnings are not always easy to grasp. In this work, we survey contemporary direct-search algorithms from a theoretical viewpoint, with the aim of highlighting the key theoretical features of these methods. We provide a basic introduction to the main classes of direct-search methods, including line-search techniques that have received little attention in earlier surveys. We also put a particular emphasis on probabilistic direct-search techniques and their application to noisy problems, a topic that has undergone significant algorithmic development in recent years. Finally, we complement existing surveys by reviewing the main theoretical advances for solving constrained and multiobjective optimization using direct-search algorithms.

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hal-05235664 , version 1 (12-02-2026)

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K.J. Dzahini, F. Rinaldi, C.W. Royer, D. Zeffiro. Direct-search methods in the year 2025: Theoretical guarantees and algorithmic paradigms. EURO Journal on Computational Optimization, 2025, 13, pp.100110. ⟨10.1016/j.ejco.2025.100110⟩. ⟨hal-05235664⟩
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