Solutions and optimality criteria for nonconvex constrained global optimization problems with connections between canonical and Lagrangian duality

David Yang Gao, Ning Ruan, Hanif D. Sherali

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36 Citations (Scopus)

Abstract

This paper presents a canonical duality theory for solving a general nonconvex quadratic minimization problem with nonconvex constraints. By using the canonical dual transformation developed by the first author, the nonconvex primal problem can be converted into a canonical dual problem with zero duality gap. A general analytical solution form is obtained. Both global and local extrema of the nonconvex problem can be identified by the triality theory associated with the canonical duality theory. Illustrative applications to quadratic minimization with multiple quadratic constraints, box/integer constraints, and general nonconvex polynomial constraints are discussed, along with insightful connections to classical Lagrangian duality. Criteria for the existence and uniqueness of optimal solutions are presented. Several numerical examples are provided.

Original languageEnglish
Pages (from-to)473-497
Number of pages25
JournalJournal of Global Optimization
Volume45
Issue number3
DOIs
Publication statusPublished - Nov 2009
Externally publishedYes

Keywords

  • Canonical duality theory
  • Global optimization
  • Integer programming
  • Lagrangian duality
  • Triality

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