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Solving Mixed-Integer Nonlinear Programs using Adaptively Refined Mixed-Integer Linear Programs

Robert Burlacu (robert.burlacu***at***fau.de)
Björn Geißler (geissler***at***developt.de)
Lars Schewe (lars.schewe***at***fau.de)

Abstract: We propose a method for solving mixed-integer nonlinear programs (MINLPs) to global optimality by discretization of occuring nonlinearities. The main idea is based on using piecewise linear functions to construct mixed-integer linear program (MIP) relaxations of the underlying MINLP. In order to find a global optimum of the given MINLP we develope 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.

Keywords: Mixed-Integer Nonlinear Programming, Piecewise Linear Approximation, Gas Transport Optimization, Global Optimization, Adaptivity

Category 1: Integer Programming ((Mixed) Integer Nonlinear Programming )

Citation: Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstraße 11, 91058 Erlangen, Germany, June 2017

Download: [PDF]

Entry Submitted: 05/23/2017
Entry Accepted: 05/23/2017
Entry Last Modified: 06/16/2017

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