Mathematical Programming

, Volume 37, Issue 1, pp 51–58

Necessary and sufficient conditions in constrained optimization

  • M. A. Hanson
  • B. Mond

DOI: 10.1007/BF02591683

Cite this article as:
Hanson, M.A. & Mond, B. Mathematical Programming (1987) 37: 51. doi:10.1007/BF02591683


Additional conditions are attached to the Kuhn-Tucker conditions giving a set of conditions which are both necessary and sufficient for optimality in constrained optimization, under appropriate constraint qualifications. Necessary and sufficient conditions are also given for optimality of the dual problem. Duality and converse duality are treated accordingly.

Key words

Necessary and sufficient conditionsKuhn-Tucker conditionsinvexity, type I and type II functionsdualityconverse duality

Copyright information

© The Mathematical Programming Society, Inc. 1987

Authors and Affiliations

  • M. A. Hanson
    • 1
  • B. Mond
    • 2
  1. 1.Department of StatisticsThe Florida State UniversityTallahasseeUSA
  2. 2.Department of MathematicsLa Trobe UniversityBundooraAustralia