Journal of Global Optimization

, Volume 64, Issue 4, pp 745–764 | Cite as

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

  • Abay Molla Kassa
  • Semu Mitiku KassaEmail author


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.


Multilevel optimization Multi-parametric programming  Convex relaxation 

Mathematics Subject Classification

90C26 90C31 91A10 90C99 65K05 



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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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Chemical and Bio Engineering, Addis Ababa Institute of TechnologyAddis Ababa UniversityAddis AbabaEthiopia
  2. 2.Department of MathematicsAddis Ababa UniversityAddis AbabaEthiopia

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