Linearization of Euclidean norm dependent inequalities applied to multibeam satellites design

Euclidean norm computations over continuous variables appear naturally in the constraints or in the objective of many problems in the optimization literature, possibly defining non-convex feasible regions or cost functions. When some other variables have discrete domains, it positions the problem in...

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Veröffentlicht in:Computational optimization and applications Jg. 73; H. 2; S. 679 - 705
Hauptverfasser: Camino, Jean-Thomas, Artigues, Christian, Houssin, Laurent, Mourgues, Stéphane
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.06.2019
Springer Nature B.V
Springer Verlag
Schlagworte:
Communication satellites
Computer Science
Continuity (mathematics)
Convex and Discrete Geometry
Domains
Integer programming
Linear programming
Linearization
Management Science
Mathematics
Mathematics and Statistics
Mixed integer
Nonlinear programming
Nonlinearity
Operations Research
Operations Research/Decision Theory
Optimization
Optimization and Control
Satellites
Statistics
Mixed Integer Nonlinear Programming
Multibeam satellites
Mixed Integer Linear Programming
center problem
Euclidean norm linearization
ISSN:0926-6003, 1573-2894
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Zusammenfassung:Euclidean norm computations over continuous variables appear naturally in the constraints or in the objective of many problems in the optimization literature, possibly defining non-convex feasible regions or cost functions. When some other variables have discrete domains, it positions the problem in the challenging Mixed Integer Nonlinear Programming (MINLP) class. For any MINLP where the nonlinearity is only present in the form of inequality constraints involving the Euclidean norm, we propose in this article an efficient methodology for linearizing the optimization problem at the cost of entirely controllable approximations even for non convex constraints. They make it possible to rely fully on Mixed Integer Linear Programming and all its strengths. We first empirically compare this linearization approach with a previously proposed linearization approach of the literature on the continuous k -center problem. This methodology is then successfully applied to a critical problem in the telecommunication satellite industry: the optimization of the beam layouts in multibeam satellite systems. We provide a proof of the NP-hardness of this very problem along with experiments on a realistic reference scenario.
Bibliographie:ObjectType-Article-1
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ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-019-00083-z