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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