Some remarks concerning duality for continuous-time programming problems
type: Item
instance of: scholarly article
title: Some remarks concerning duality for continuous-time programming problems
zbMATH Open document ID: 0604.90135
DOI: 10.1016/0022-247X(86)90100-9
author: R. N. Buie
author: Jaromir Abrham
published in: Journal of Mathematical Analysis and Applications
publication date: 1986-01-01T00:00:00Z
review text: Several researchers have studied duality in continuous-time programming. In earlier works there have been problems in duality theorems with the representation of dual variables. In the spaces previously used, very strong conditions have been imposed on the problem to ensure the existence of dual variables. In the simple counterexample of Grinold in continuous-time linear programming the primal problem has an optimal solution and feasible dual solutions but no optimal dual solution. This paper proposes that in the dual problem Lebesgue-Stieltjes integration should be employed in place of Lebesgue integration. In this way the authors are able to obtain results analogous to classical linear and nonlinear duality theory. They also can help in explaining enigmas caused by such problems of Grinold's counterexample.
Mathematics Subject Classification ID: 90C99
Mathematics Subject Classification ID: 49L99
Mathematics Subject Classification ID: 49N15
zbMATH DE Number: 3976815
zbMATH Keywords: duality
zbMATH Keywords: continuous-time programming
zbMATH Keywords: Lebesgue-Stieltjes integration
reviewed by: István Maros
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3976815