Adaptive piecewise linear relaxations for enclosure computations for nonconvex multiobjective mixed-integer quadratically constrained programs

Link, Moritz; Volkwein, Stefan

Adaptive piecewise linear relaxations for enclosure computations for nonconvex multiobjective mixed-integer quadratically constrained programs

Dateien

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Datum

2023

Open Access-Veröffentlichung

Open Access Hybrid

Sammlungen

Mathematik und Statistik

Publikationstyp

Zeitschriftenartikel

Publikationsstatus

Published

Erschienen in

Journal of Global Optimization. Springer. 2023, 87(1), pp. 97-132. ISSN 0925-5001. eISSN 1573-2916. Available under: doi: 10.1007/s10898-023-01309-5

Zusammenfassung

In this paper, a new method for computing an enclosure of the nondominated set of multiobjective mixed-integer quadratically constrained programs without any convexity requirements is presented. In fact, our criterion space method makes use of piecewise linear relaxations in order to bypass the nonconvexity of the original problem. The method chooses adaptively which level of relaxation is needed in which parts of the image space. Furthermore, it is guaranteed that after finitely many iterations, an enclosure of the nondominated set of prescribed quality is returned. We demonstrate the advantages of this approach by applying it to multiobjective energy supply network problems.

Fachgebiet (DDC)

510 Mathematik

Schlagwörter

Mixed-integer nonlinear programming, Multiobjective optimization, Box enclosure, Adaptive piecewise linear relaxation, Energy supply networks

Zitieren

ISO 690

LINK, Moritz, Stefan VOLKWEIN, 2023. Adaptive piecewise linear relaxations for enclosure computations for nonconvex multiobjective mixed-integer quadratically constrained programs. In: Journal of Global Optimization. Springer. 2023, 87(1), pp. 97-132. ISSN 0925-5001. eISSN 1573-2916. Available under: doi: 10.1007/s10898-023-01309-5

BibTex

@article{Link2023-07-05Adapt-67484,
  year={2023},
  doi={10.1007/s10898-023-01309-5},
  title={Adaptive piecewise linear relaxations for enclosure computations for nonconvex multiobjective mixed-integer quadratically constrained programs},
  number={1},
  volume={87},
  issn={0925-5001},
  journal={Journal of Global Optimization},
  pages={97--132},
  author={Link, Moritz and Volkwein, Stefan}
}

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