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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Vydáno v:Journal of mathematical analysis and applications Ročník 437; číslo 1; s. 1 - 15
Hlavní autoři: Vinh, N.T., Kim, D.S., Tam, N.N., Yen, N.D.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Inc 01.05.2016
Témata:
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
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Shrnutí: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