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

Burlacu R, Geiβler B, Schewe L (2019)

Publication Type: Journal article

Publication year: 2019

Journal

Optimization Methods & Software Taylor & Francis: STM, Behavioural Science and Public Health Titles / Taylor & Francis

DOI: 10.1080/10556788.2018.1556661

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.

Authors with CRIS profile

Robert Burlacu Economics - Discrete Optimization - Mathematics (EDOM) Lars Schewe Naturwissenschaftliche Fakultät

How to cite

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).

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