A sufficient and necessary condition for nonconvex constrained optimization

C. J. Goh, Xiaoqi Yang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

14 Citations (Scopus)


The conventional Lagrangian approach to solving constrained optimization problems leads to optimally conditions which are either necessary, or sufficient, but not both unless the underlying cost and constraint functions are also convex. We introduce a new approach based on the Tchebyshev norm. This leads to an optimality condition which is both sufficient and necessary, without any convexity assumption. This optimality condition can be used to devise a conceptually simple method for solving nonconvex inequality constrained optimization problems.
Original languageEnglish
Pages (from-to)9-12
Number of pages4
JournalApplied Mathematics Letters
Issue number5
Publication statusPublished - 12 Sep 1997
Externally publishedYes


  • Equivalent optimality condition
  • Inequality constraints
  • Nonconvex optimization

ASJC Scopus subject areas

  • Applied Mathematics

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