Derivative-free methods for mixed-integer nonsmooth constrained optimization

In this paper, mixed-integer nonsmooth constrained optimization problems are considered, where objective/constraint functions are available only as the output of a black-box zeroth-order oracle that does not provide derivative information. A new derivative-free linesearch-based algorithmic framework...

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Bibliographic Details
Published in:Computational optimization and applications Vol. 82; no. 2; pp. 293 - 327
Main Authors: Giovannelli, Tommaso, Liuzzi, Giampaolo, Lucidi, Stefano, Rinaldi, Francesco
Format: Journal Article
Language:English
Published: New York Springer US 01.06.2022
Springer Nature B.V
Subjects:
Algorithms
Constraints
Convex and Discrete Geometry
Derivatives
Management Science
Mathematics
Mathematics and Statistics
Mixed integer
Operations Research
Operations Research/Decision Theory
Optimization
Statistics
Variables
Nonsmooth optimization
65K05
Mixed-integer nonlinear programming
90C11
90C56
Derivative-free optimization
ISSN:0926-6003, 1573-2894
Online Access:Get full text
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Summary:In this paper, mixed-integer nonsmooth constrained optimization problems are considered, where objective/constraint functions are available only as the output of a black-box zeroth-order oracle that does not provide derivative information. A new derivative-free linesearch-based algorithmic framework is proposed to suitably handle those problems. First, a scheme for bound constrained problems that combines a dense sequence of directions to handle the nonsmoothness of the objective function with primitive directions to handle discrete variables is described. Then, an exact penalty approach is embedded in the scheme to suitably manage nonlinear (possibly nonsmooth) constraints. Global convergence properties of the proposed algorithms toward stationary points are analyzed and results of an extensive numerical experience on a set of mixed-integer test problems are reported.
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ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-022-00363-1