Solving mixed-integer nonlinear programmes using adaptively refined mixed-integer linear programmes

Beitrag in einer Fachzeitschrift


Details zur Publikation

Autorinnen und Autoren: Burlacu R, Geiβler B, Schewe L
Zeitschrift: Optimization Methods & Software
Jahr der Veröffentlichung: 2019
ISSN: 1055-6788


Abstract

We propose a method for solving mixed-integer nonlinear programmes (MINLPs) to global optimality by discretization of occurring nonlinearities. The main idea is based on using piecewise linear functions to construct mixed-integer linear programme (MIP) relaxations of the underlying MINLP. In order to find a global optimum of the given MINLP, we develop an iterative algorithm which solves MIP relaxations that are adaptively refined. We are able to give convergence results for a wide range of MINLPs requiring only continuous nonlinearities with bounded domains and an oracle computing maxima of the nonlinearities on their domain. Moreover, the practicalness of our approach is shown numerically by an application from the field of gas network optimization.


FAU-Autorinnen und Autoren / FAU-Herausgeberinnen und Herausgeber

Burlacu, Robert
Lehrstuhl für Angewandte Mathematik (Gemischt-ganzzahlige lineare und nichtlineare Optimierung)
Schewe, Lars PD Dr.
Naturwissenschaftliche Fakultät


Zitierweisen

APA:
Burlacu, R., Geiβler, B., & Schewe, L. (2019). Solving mixed-integer nonlinear programmes using adaptively refined mixed-integer linear programmes. Optimization Methods & Software. https://dx.doi.org/10.1080/10556788.2018.1556661

MLA:
Burlacu, Robert, Björn Geiβler, and Lars Schewe. "Solving mixed-integer nonlinear programmes using adaptively refined mixed-integer linear programmes." Optimization Methods & Software (2019).

BibTeX: 

Zuletzt aktualisiert 2019-20-08 um 16:23