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

Abay Molla Kassa, Semu Mitiku Kassa

    Research output: Contribution to journalArticle

    7 Citations (Scopus)

    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.

    Original languageEnglish
    Pages (from-to)745-764
    Number of pages20
    JournalJournal of Global Optimization
    Volume64
    Issue number4
    DOIs
    Publication statusPublished - 2016

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    Parametric Programming
    Nonlinear programming
    Branch-and-bound
    Global optimization
    Non-convexity
    Optimization
    Multilevel Programming
    Convex Relaxation
    Global Optimum
    Subdivision
    Nonlinear Programming
    Global Optimization
    Parameter Space
    Partitioning
    Formulation
    Term
    Programming

    All Science Journal Classification (ASJC) codes

    • Computer Science Applications
    • Control and Optimization
    • Management Science and Operations Research
    • Applied Mathematics

    Cite this

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    AB - 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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