Duality gap function in infinite dimensional linear programming

The concept of duality gap function in infinite dimensional linear programming is considered in this paper. Basic properties of the function and two theorems on its behavior are obtained by using duality theorems with interior conditions. As illustrations for the results, we investigate the parametr...

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Bibliographic Details
Published in:	Journal of mathematical analysis and applications Vol. 437; no. 1; pp. 1 - 15
Main Authors:	Vinh, N.T., Kim, D.S., Tam, N.N., Yen, N.D.
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 01.05.2016
Subjects:	Duality gap function Duality theorems Function of bounded variation Infinite dimensional linear programming Interior point Riemann–Stieltjes integral Duality theorems Duality gap function Interior point Function of bounded variation Infinite dimensional linear programming Riemann–Stieltjes integral
ISSN:	0022-247X, 1096-0813
Online Access:	Get full text
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Summary:	The concept of duality gap function in infinite dimensional linear programming is considered in this paper. Basic properties of the function and two theorems on its behavior are obtained by using duality theorems with interior conditions. As illustrations for the results, we investigate the parametric versions of an example due to D. Gale and parametric linear programs on spaces of continuous functions. The notions of Riemann–Stieltjes integral and function of bounded variation have been shown to be very useful for our investigations.
ISSN:	0022-247X 1096-0813
DOI:	10.1016/j.jmaa.2015.12.043