On Symmetric Duality in Nonlinear Programming

M. S. Bazaraa and J. J. Goode
Additional contact information
M. S. Bazaraa: Georgia Institute of Technology, Atlanta, Georgia
J. J. Goode: Georgia Institute of Technology, Atlanta, Georgia

Operations Research, 1973, vol. 21, issue 1, 1-9

Abstract: In this study we generalize the formulation of symmetric duality introduced by Dantzig, Eisenberg, and Cottle to include the case where the constraints of the inequality type are defined via closed convex cones and their polars. The new formulation retains the symmetric properties of the original programs. Under suitable convexity/concavity assumptions we generalize the known results about symmetric duality. The case where the function involved is strongly convex/strongly concave is also treated and Karamardian's result in this case is generalized. As a result, we show that every strongly convex function achieves a minimum value over any closed convex cone at a unique point. Some special cases of symmetric programs are then considered, leading to generalizations of Wolfe's duality as well as generalizations of quadratic and linear programming formulations.

Date: 1973
References: Add references at CitEc
Citations: View citations in EconPapers (22)

Downloads: (external link)
http://dx.doi.org/10.1287/opre.21.1.1 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:21:y:1973:i:1:p:1-9

Access Statistics for this article

More articles in Operations Research from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().