Properties, Extensions and Application of Piecewise Linearization for Euclidean Norm Optimization in R2

This work considers nonconvex mixed integer nonlinear programming where nonlinearity comes from the presence of the two-dimensional euclidean norm in the objective or the constraints. We build from the euclidean norm piecewise linearization proposed by Camino et al. (Comput. Optim. Appl. https://doi...

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Bibliographic Details
Published in:Journal of optimization theory and applications 2022-11, Vol.195 (2), p.418-448
Main Authors: Duguet, Aloïs, Artigues, Christian, Houssin, Laurent, Ngueveu, Sandra Ulrich
Format: Article
Language:English
Subjects:
Applications of Mathematics
Approximation
Calculus of Variations and Optimal Control
Optimization
Engineering
Industrial applications
Integer programming
Linear programming
Linearization
Mathematical analysis
Mathematics
Mathematics and Statistics
Mixed integer
Nonlinear programming
Nonlinearity
Operations Research/Decision Theory
Optimization
Satellites
Theory of Computation
Variables
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Summary:This work considers nonconvex mixed integer nonlinear programming where nonlinearity comes from the presence of the two-dimensional euclidean norm in the objective or the constraints. We build from the euclidean norm piecewise linearization proposed by Camino et al. (Comput. Optim. Appl. https://doi.org/10.1007/s10589-019-00083-z , 2019) that allows to solve such nonconvex problems via mixed-integer linear programming with an arbitrary approximation guarantee. Theoretical results are established that prove that this linearization is able to satisfy any given approximation level with the minimum number of pieces. An extension of the piecewise linearization approach is proposed. It shares the same theoretical properties for elliptic constraints and/or objective. An application shows the practical appeal of the elliptic linearization on a nonconvex beam layout mixed optimization problem coming from an industrial application.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-022-02083-2