Accession Number : ADA019584

Title :   The Complementary Unboundedness of Dual Feasible Solution Sets in Convex Programming,

Corporate Author : NORTHWESTERN UNIV EVANSTON ILL DEPT OF INDUSTRIAL ENGINEERING AND MANAGEMENT SCIENCES

Personal Author(s) : Peterson,Elmor L.

Report Date : AUG 1975

Pagination or Media Count : 29

Abstract : F. E. Clark has shown that if at least one of the feasible solution sets for a pair of dual linear programming problems is nonempty then at least one of them is both nonempty and unbounded. Subsequently, M. Avriel and A. C. Williams have obtained the same result in the more general context of (prototype posynomial) geometric programming. In this paper it is shown that the same result is actually false in the even more general context of convex programming - unless a certain regularity condition is satisfied. It is also shown that the regularity condition is so weak that it is automatically satisfied in linear programming, (prototype posynomial) geometric programming, quadratic programming (with either linear or quadratic constraints), l sub p -regression analysis, optimal location, roadway network analysis, and chemical equilibrium analysis. Moreover, the author develops an equivalent regularity condition for each of the usual formulations of duality.

Descriptors :   *Linear programming, Convex sets, Theorems

Subject Categories : Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE