Global Optimization of Nonlinear Bilevel Programming Problems

Zeynep H. Gümüş, Christodoulos A. Floudas

Research output: Contribution to journalArticlepeer-review

129 Scopus citations

Abstract

A novel technique that addresses the solution of the general nonlinear bilevel programming problem to global optimality is presented. Global optimality is guaranteed for problems that involve twice differentiable nonlinear functions as long as the linear independence constraint qualification condition holds for the inner problem constraints. The approach is based on the relaxation of the feasible region by convex underestimation, embedded in a branch and bound framework utilizing the basic principles of the deterministic global optimization algorithm, αBB [2, 4, 5, 11]. Epsilon global optimality in a finite number of iterations is theoretically guaranteed. Computational studies on several literature problems are reported.

Original languageEnglish
Pages (from-to)1-31
Number of pages31
JournalJournal of Global Optimization
Volume20
Issue number1
DOIs
StatePublished - May 2001
Externally publishedYes

Keywords

  • Bilevel nonlinear
  • Bilevel optimization
  • Bilevel programming
  • Global optimization
  • Mixed integer nonlinear optimization
  • Nonconvex
  • Twice-continuously differentiable

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