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

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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.

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Acknowledgments

This work is in part supported by the Swedish International Science Program (ISP), through the project at the Department of Mathematics, Addis Ababa University. The authors also would like to thank the anonymous referees from whom we received valuable comments and suggestions to improve the earlier version of the manuscript.

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Authors and Affiliations

  1. Department of Chemical and Bio Engineering, Addis Ababa Institute of Technology, Addis Ababa University, P.O. Box 385, Addis Ababa, Ethiopia

    Abay Molla Kassa

  2. Department of Mathematics, Addis Ababa University, P.O. Box 1176, Addis Ababa, Ethiopia

    Semu Mitiku Kassa

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  1. Abay Molla Kassa
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  2. Semu Mitiku Kassa
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Correspondence to Semu Mitiku Kassa.

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Kassa, A.M., Kassa, S.M. A branch-and-bound multi-parametric programming approach for non-convex multilevel optimization with polyhedral constraints. J Glob Optim 64, 745–764 (2016). https://doi.org/10.1007/s10898-015-0341-0

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