Skip to main content
Log in

Optimality condition: Constraint regularization

  • Published:
Mathematical Programming Submit manuscript

Abstract

Necessity and sufficiency conditions are given for the existence of a finite set of redundant constraints which together with a given set of constraints in an optimization problem satisfy the Kuhn—Tucker, and the Guignard Constraint qualifications when the original set of constraints fails to satisfy either or both of them.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. J. Abadie, “On the Kuhn—Tucker theorem”, in: J. Abadie, ed.,Nonlinear programming (North-Holland, Amsterdam, 1967) 19–36.

    Google Scholar 

  2. K.J. Arrow, L. Hurwicz and H. Uzawa, “Constraint qualifications in maximization problems”,Naval Research Logistic Quarterly 8 (1961) 175–191.

    Google Scholar 

  3. M.S. Bazaraa, J.J. Goode and C.M. Shetty, “Constraint qualifications revisited”,Management Science 18 (1972) 567–573.

    Google Scholar 

  4. R.W. Cottle, “A theorem of Fritz—John in mathematical programming”, RAND Memo. RM-3858-PR. The Rand Corporation, Santa Monica, CA (1963).

    Google Scholar 

  5. J. Evans, “A note on constraint qualifications”,Rep. 6917, Center for Mathematical Studies in Business and Economics, Graduate School of Business, Univ. of Chicago (1969).

  6. W. Fenchel,Convex cones, sets and functions (University Press, Princeton, 1953).

    Google Scholar 

  7. D. Gale,The theory of linear economic models (McGraw-Hill, New York, 1960) pp. 59–60.

    Google Scholar 

  8. F. Gould and J. Tolle, “A necessary and sufficient qualification for constrained optimization”,SIAM Journal on Applied Mathematics 20 (1971) 164–172.

    Google Scholar 

  9. F. Gould and J. Tolle, “Geometry of optimality conditions and constraint qualifications”,Mathematical Programming 2 (1972) 1–18.

    Google Scholar 

  10. M. Guignard, “Conditions d'optimalité et dualité en programmation mathématique”, Thèse, Université de Lille (1967).

  11. M. Guignard, “Generalized Kuhn—Tucker conditions for mathematical programming problems in Banach space”,SIAM Journal on Control 7 (1969) 232–241.

    Google Scholar 

  12. H. Kuhn and A. Tucker, “Nonlinear programming”, in: J. Neyman, ed.,Proc. Second Berkeley Symposium on Mathematical Statistics and Probability (University of California Press, Berkeley, 1951) pp. 481–492.

    Google Scholar 

  13. O.L. Mangasarian,Nonlinear programming (McGraw-Hill, New York, 1969).

    Google Scholar 

  14. O.L. Mangasarian and S. Fromovitz, “The Fritz—John necessary optimality conditions in the presence of equality and inequality constraints”,Journal of Mathematical Analysis and Applications 17 (1967) 37–47.

    Google Scholar 

  15. S. Vajda, “Test of optimality in constrained optimization”,Journal of the Institute of Mathematics and Its Applications 13 (1974) 187–200.

    Google Scholar 

  16. S. Vajda,Theory of linear and nonlinear programming (Longman, London, 1974).

    Google Scholar 

  17. P. Varaiya, “Nonlinear programming in Banach space”,SIAM Journal on Applied Mathematics 15 (1967) 284–293.

    Google Scholar 

  18. W.I. Zangwill,Nonlinear programming: a unified approach (Prentice Hall, Englewood Cliffs, NJ, 1969).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

This work was carried out at the Department of Statistics, University College of Wales, Aberystwyth while the author was sponsored by the Commonwealth Scholarship Commission in the United Kingdom, through the Department of Statistics, University of Nigeria, Nsukka.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Agunwamba, C.C. Optimality condition: Constraint regularization. Mathematical Programming 13, 38–48 (1977). https://doi.org/10.1007/BF01584322

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01584322

Key words

Navigation