Schmidt, Martin ; Sirvent, Mathias ; Wollner, Winnifried (2024)
The cost of not knowing enough: mixed-integer optimization with implicit Lipschitz nonlinearities.
In: Optimization Letters, 2022, 16 (5)
doi: 10.26083/tuprints-00023533
Artikel, Zweitveröffentlichung, Verlagsversion
 | Es ist eine neuere Version dieses Eintrags verfügbar. |
Kurzbeschreibung (Abstract)
It is folklore knowledge that nonconvex mixed-integer nonlinear optimization problems can be notoriously hard to solve in practice. In this paper we go one step further and drop analytical properties that are usually taken for granted in mixed-integer nonlinear optimization. First, we only assume Lipschitz continuity of the nonlinear functions and additionally consider multivariate implicit constraint functions that cannot be solved for any parameter analytically. For this class of mixed-integer problems we propose a novel algorithm based on an approximation of the feasible set in the domain of the nonlinear function—in contrast to an approximation of the graph of the function considered in prior work. This method is shown to compute approximate global optimal solutions in finite time and we also provide a worst-case iteration bound. In some first numerical experiments we show that the “cost of not knowing enough” is rather high by comparing our approach with the open-source global solver SCIP. This reveals that a lot of work is still to be done for this highly challenging class of problems and we thus finally propose some possible directions of future research.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2024 |
| Autor(en): | Schmidt, Martin ; Sirvent, Mathias ; Wollner, Winnifried |
| Art des Eintrags: | Zweitveröffentlichung |
| Titel: | The cost of not knowing enough: mixed-integer optimization with implicit Lipschitz nonlinearities |
| Sprache: | Englisch |
| Publikationsjahr: | 2 April 2024 |
| Ort: | Darmstadt |
| Publikationsdatum der Erstveröffentlichung: | Juni 2022 |
| Ort der Erstveröffentlichung: | Berlin ; Heidelberg |
| Verlag: | Springer |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Optimization Letters |
| Jahrgang/Volume einer Zeitschrift: | 16 |
| (Heft-)Nummer: | 5 |
| DOI: | 10.26083/tuprints-00023533 |
| URL / URN: | https://tuprints.ulb.tu-darmstadt.de/23533 |
| Zugehörige Links: | |
| Herkunft: | Zweitveröffentlichung DeepGreen |
| Kurzbeschreibung (Abstract): | It is folklore knowledge that nonconvex mixed-integer nonlinear optimization problems can be notoriously hard to solve in practice. In this paper we go one step further and drop analytical properties that are usually taken for granted in mixed-integer nonlinear optimization. First, we only assume Lipschitz continuity of the nonlinear functions and additionally consider multivariate implicit constraint functions that cannot be solved for any parameter analytically. For this class of mixed-integer problems we propose a novel algorithm based on an approximation of the feasible set in the domain of the nonlinear function—in contrast to an approximation of the graph of the function considered in prior work. This method is shown to compute approximate global optimal solutions in finite time and we also provide a worst-case iteration bound. In some first numerical experiments we show that the “cost of not knowing enough” is rather high by comparing our approach with the open-source global solver SCIP. This reveals that a lot of work is still to be done for this highly challenging class of problems and we thus finally propose some possible directions of future research. |
| Freie Schlagworte: | Mixed-integer nonlinear optimization, Global optimization, Lipschitz optimization, Gas networks |
| Status: | Verlagsversion |
| URN: | urn:nbn:de:tuda-tuprints-235336 |
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
| Fachbereich(e)/-gebiet(e): | 04 Fachbereich Mathematik 04 Fachbereich Mathematik > Optimierung |
| Hinterlegungsdatum: | 02 Apr 2024 11:23 |
| Letzte Änderung: | 03 Apr 2024 05:14 |
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| Suche nach Titel in: | TUfind oder in Google |
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- The cost of not knowing enough: mixed-integer optimization with implicit Lipschitz nonlinearities. (deposited 02 Apr 2024 11:23) [Gegenwärtig angezeigt]
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