Technical Note—A Duality Theory for Convex Programming with Set-Inclusive Constraints

A. L. Soyster
Additional contact information
A. L. Soyster: Temple University, Philadelphia, Pennsylvania

Operations Research, 1974, vol. 22, issue 4, 892-898

Abstract: This paper extends the notion of convex programming with set-inclusive constraints as set forth by Soyster [ Opns. Res. 21, 1154–1157 (1973)] by replacing the objective vector c with a convex set C and formulating a dual problem. The primal problem to be considered is \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland,xspace}\usepackage{amsmath,amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$$\sup\Bigl\{\inf_{c\in C} c \cdot x \mid x_{1}K_{1}+x_{2}K_{2}+ \ldots x_{n}K_{n}\subseteq K(b), x_{i}\geq 0\Bigr\}$$\end{document} where the sets { K j } are convex activity sets, K ( b ) is a polyhedral resource set, C is a convex set of objective vectors, and the binary operation + refers to addition of sets. Any feasible solution to the dual problem provides an upper bound to (I) and, at optimality conditions, the value of (I) is equal to the value of the dual. Furthermore, the optimal solution of the dual problem can be used to reduce (I) to an ordinary linear programming problem.

Date: 1974
References: Add references at CitEc
Citations: View citations in EconPapers (7)

Downloads: (external link)
http://dx.doi.org/10.1287/opre.22.4.892 (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:22:y:1974:i:4:p:892-898

Access Statistics for this article

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