Deterministic solution approach for some classes of nonlinear multilevel programs with multiple followers

Journal 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: 2017

Journal: Journal of Global Optimization (0925-5001)

Journal acronym: J GLOBAL OPTIM

Volume number: 68

Issue number: 4

Start page: 729

End page: 747

Number of pages: 19

ISSN: 0925-5001

eISSN: 1573-2916

Languages: English-Great Britain (EN-GB)

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Abstract

In this paper we investigate multilevel programming problems with multiple followers in each hierarchical decision level. It is known that such type of problems are highly non-convex and hard to solve. A solution algorithm have been proposed by reformulating the given multilevel program with multiple followers at each level that share common resources into its equivalent multilevel program having single follower at each decision level. Even though, the reformulated multilevel optimization problem may contain non-convex terms at the objective functions at each level of the decision hierarchy, we applied multi-parametric branch-and-bound algorithm to solve the resulting problem that has polyhedral constraints. The solution procedure is implemented and tested for a variety of illustrative examples.

Keywords

Hierarchical decision, Multilevel programs with multiple followers, Multilevel programs with single follower, Nash equilibrium, Parametric optimization

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