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

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 constr...

Full description

Saved in:
Bibliographic Details
Published inMathematical programming computation Vol. 16; no. 3; pp. 369 - 422
Main Authors Torres, Juan J., Nannicini, Giacomo, Traversi, Emiliano, Wolfler Calvo, Roberto
Format Journal Article
LanguageEnglish
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
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:1867-2949
1867-2957
DOI:10.1007/s12532-024-00260-0