Mathematical Programming

, Volume 37, Issue 1, pp 51–58 | Cite as

Necessary and sufficient conditions in constrained optimization

  • M. A. Hanson
  • B. Mond


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 conditions Kuhn-Tucker conditions invexity, type I and type II functions duality converse duality 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    M. A. Hanson, “On sufficiency of the Kuhn-Tucker conditions”,Journal of Mathematical Analysis and Applications 80 (1981) 545–550.MATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    M. A. Hanson and B. Mond, “Further generalizations of convexity in mathematical programming”,Journal of Information and Optimization Sciences (1982) 25–32.Google Scholar
  3. [3]
    B. Mond and M. A. Hanson, “On duality with generalized convexity”,Mathematische Operationsforschung und Statistik Series Optimization 15 (1984) 313–317.MATHMathSciNetGoogle Scholar
  4. [4]
    O.L. Mangasarian,Nonlinear Programming (McGraw-Hill, New York, 1969).MATHGoogle Scholar
  5. [5]
    M.A. Hanson, “A duality theorem in nonlinear programming with nonlinear constraints”,Australian Journal of Statistics 3 (1961) 67–71.MathSciNetCrossRefGoogle Scholar
  6. [6]
    P. Huard, “Dual programs”,IBM Journal of Research and Development 6 (1962) 137–139.MATHCrossRefGoogle Scholar
  7. [7]
    A. Ben-Israel and B. Mond, “What is invexity?”Journal of the Australian Mathematical Society Series B 28 (1986) 1–9.MATHMathSciNetCrossRefGoogle Scholar
  8. [8]
    R.M. Thrall and L. Tornheim,Vector Spaces and Matrices (Wiley, New York, 1957).MATHGoogle Scholar

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

Personalised recommendations