A trust-region framework for derivative-free mixed-integer optimization

• Published in: Mathematical programming computation Vol. 16; no. 3; pp. 369 - 422
• Main Authors: Torres, Juan J., Nannicini, Giacomo, Traversi, Emiliano, Wolfler Calvo, Roberto
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2024
• Subjects: Full Length Paper; Mathematics; Mathematics and Statistics; Mathematics of Computing; Operations Research/Decision Theory; Optimization; Theory of Computation; 90C30; Mixed-integer programming; 90C11; 90C56; Nonlinear programming; Trust-region methods; Derivative-free optimization
• ISSN: 1867-2949; 1867-2957
• DOI: 10.1007/s12532-024-00260-0

This paper overviews the development of a framework for the optimization of black-box mixed-integer functions subject to bound constraints. Our methodology is based on the use of tailored surrogate approximations of the unknown objective function, in combination with a trust-region method. To construct suitable model approximations, we assume that the unknown objective is locally quadratic, and we prove that this leads to fully-linear models in restricted discrete neighborhoods. We show that the proposed algorithm converges to a first-order mixed-integer stationary point according to several natural definitions of mixed-integer stationarity, depending on the structure of the objective function. We present numerical results to illustrate the computational performance of different implementations of this methodology in comparison with the state-of-the-art derivative-free solver NOMAD.