Skip to main content
Log in

On interior and convexity conditions, development of dual problems and saddlepoint optimality criteria in abstract mathematical programming

  • Published:
Mathematical Programming Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

In this paper, duality is studied as a consequence of separating certain derived sets related to optimization problems. The interior and convexity conditions used and two groups of related derived sets are studied and a new interior condition for duality arises quite naturally. Several dual problems are presented and the paper is concluded by presentation of saddlepoint optimality criteria for the problems considered.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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. D.G. Luenberger,Optimization by vector space methods (Wiley, New York, 1969).

    Google Scholar 

  2. D.A. Pyne, “On interior and convexity conditions, development of dual criteria in abstract mathematical programming”, Tech. Rept. No. 175, Department of Mathematical Sciences, The Johns Hopkins University, Baltimore, Md. (1973).

    Google Scholar 

  3. V.A. Sposito and H.T. David, “Saddlepoint optimality criteria of nonlinear programming problems over cones without differentiability”,SIAM Journal on Applied Mathematics 20 (1971) 698–702.

    Google Scholar 

  4. R.M. Van Slyke and R.J.-B. Wets, “A duality theory for abstract programs with applications to optimal control theory”,Journal of Mathematical Applications and Analysis 22 (1968) 679–706.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pyne, D.A. On interior and convexity conditions, development of dual problems and saddlepoint optimality criteria in abstract mathematical programming. Mathematical Programming 8, 125–133 (1975). https://doi.org/10.1007/BF01580438

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01580438

Keywords

Navigation