A standard branch-and-bound approach for nonlinear semi-infinite problems

•Branch and bound algorithm for non-convex semi-infinite problems.•Extension of classical bounding technics to such semi-infinite problems.•Interval evaluations of semi-infinite constraints and their generalized gradient.•Open-source distributed implementation of the algorithm (http://www.ibex-lib.o...

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Bibliographic Details
Published in:European journal of operational research Vol. 282; no. 2; pp. 438 - 452
Main Authors: Marendet, Antoine, Goldsztejn, Alexandre, Chabert, Gilles, Jermann, Christophe
Format: Journal Article
Language:English
Published: Elsevier B.V 16.04.2020
Elsevier
Subjects:
Branch-and-bound
Computer Science
Constraint programming
Mathematics
Numerical Analysis
Optimization and Control
Relaxation
Restriction
Semi-infinite programming
Semi-infinite programming
Branch-and-bound
Relaxation
Restriction
Constraint programming
restriction
branch-and-bound
constraint programming
relaxation
ISSN:0377-2217, 1872-6860
Online Access:Get full text
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Summary:•Branch and bound algorithm for non-convex semi-infinite problems.•Extension of classical bounding technics to such semi-infinite problems.•Interval evaluations of semi-infinite constraints and their generalized gradient.•Open-source distributed implementation of the algorithm (http://www.ibex-lib.org/). This paper considers nonlinear semi-infinite problems, which contain at least one semi-infinite constraint (SIC). The standard branch-and-bound algorithm is adapted to such problems by extending usual upper and lower bounding techniques for nonlinear inequality constraints to SICs. This is achieved by defining the interval evaluation of parametrized functions and their generalized gradients, by also adapting numerical constraint programming techniques to quantified inequalities, and by introducing linear relaxations and restrictions for SICs. The overall efficiency of our algorithm is demonstrated on a standard set of benchmarks from the literature, in comparison with the best state of the art alternative.
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2019.10.025