ISSN:
1436-4646
Keywords:
Complementary Unboundedness
;
Dual Feasible Solution Sets
;
Convex Programming
;
Geometric Programming
;
Fenchel Duality
;
Rockafellar Duality
;
Ordinary Duality
;
Quadratic Programming
;
Optimal Location
;
Traffic Equilibria
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
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 we show that the same result is actually false in the even more general context of convex programming — unless a certain regularity condition is satisfied. We also show 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 p -regression analysis, optimal location, roadway network analysis, and chemical equilibrium analysis. Moreover, we develop an equivalent regularity condition for each of the usual formulations of duality.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01593806
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