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<p>In this work, we propose <i>Model-and-Search</i> (MAS), a novel local-search derivative-free optimization algorithm, and show that it is convergent to a Karush-Kuhn-Tucker point. MAS aims to optimize a deterministic function over a box-bounded domain and is designed to work well within a confined budget of function evaluations. In MAS, the search is oriented to improve the value of the incumbent by combining a set of techniques, including gradient estimation and quadratic model building and optimization. We propose a novel sensitivity-based approach to construct an incomplete quadratic model when points are not enough to build a complete quadratic surrogate model of the true function. The surrogate model is then used to guide the search. We present extensive computational results on a collection of 501 publicly available test problems with varying dimensions and complexity. The computational results demonstrate that MAS performs well regardless of problem convexity and smoothness.</p>

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Model-and-search: a derivative-free local optimization algorithm

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年5月11日

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  • Kaiwen Ma,
  • Luis Miguel Rios,
  • Hua Zheng,
  • Nikolaos V. Sahinidis,
  • Sreekanth Rajagopalan

摘要

In this work, we propose Model-and-Search (MAS), a novel local-search derivative-free optimization algorithm, and show that it is convergent to a Karush-Kuhn-Tucker point. MAS aims to optimize a deterministic function over a box-bounded domain and is designed to work well within a confined budget of function evaluations. In MAS, the search is oriented to improve the value of the incumbent by combining a set of techniques, including gradient estimation and quadratic model building and optimization. We propose a novel sensitivity-based approach to construct an incomplete quadratic model when points are not enough to build a complete quadratic surrogate model of the true function. The surrogate model is then used to guide the search. We present extensive computational results on a collection of 501 publicly available test problems with varying dimensions and complexity. The computational results demonstrate that MAS performs well regardless of problem convexity and smoothness.