Duality gap function in infinite dimensional linear programming

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:437

Article

Vinh, N. T.¹  Kim, D. S.²  Tam, N. N.³  Yen, N. D.¹ 

[1] Vietnam Acad Sci & Technol, Inst Math, 18 Hoang Quoc Viet, Hanoi 10307, Vietnam

[2] Pukyong Natl Univ, Dept Appl Math, Busan 608787, South Korea

[3] Hanoi Pedag Inst, Dept Math, 2 Xuan Hoa, Me Linh, Vinh Phuc, Vietnam

关键词: Infinite dimensional linear programming;    Duality theorems;    Duality gap function;    Interior point;    Riemann-Stieltjes integral;    Function of bounded variation;   

DOI  :  10.1016/j.jmaa.2015.12.043

来源: Elsevier

【 摘 要 】

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. (C) 2015 Published by Elsevier Inc.

【 授权许可】

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