A branch-and-bound multi-parametric programming approach for non-convex multilevel optimization with polyhedral constraints

Conference proceedings article

Authors/Editors

Kassa, Semu

Research Areas

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Publication Details

Author list: Kassa AM, Kassa SM

Publisher: Springer Verlag (Germany)

Place: DORDRECHT

Publication year: 2016

Journal: Journal of Global Optimization (0925-5001)

Journal acronym: J GLOBAL OPTIM

Volume number: 64

Issue number: 4

Start page: 745

End page: 764

Number of pages: 20

ISSN: 0925-5001

eISSN: 1573-2916

Languages: English-Great Britain (EN-GB)

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Abstract

In this paper we develop a general but smooth global optimization strategy for nonlinear multilevel programming problems with polyhedral constraints. At each decision level successive convex relaxations are applied over the non-convex terms in combination with a multi-parametric programming approach. The proposed algorithm reaches the approximate global optimum in a finite number of steps through the successive subdivision of the optimization variables that contribute to the non-convexity of the problem and partitioning of the parameter space. The method is implemented and tested for a variety of bilevel, trilevel and fifth level problems which have non-convexity formulation at their inner levels.

Keywords

Convex relaxation, Multilevel optimization, Multi-parametric programming

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