Date Log
WOLFE TYPE DUALITY FOR LINEAR OPTIMIZATION PROBLEMS WITH EQUILIBRIUM CONSTRAINTS
Corresponding Author(s) : Tran Van Su
UED Journal of Social Sciences, Humanities and Education,
Vol. 8 No. 4 (2018): UED JOURNAL OF SOCIAL SCIENCES, HUMANITIES AND EDUCATION
Abstract
Duality has an important role in the study of mathematical programming problems , since the weak duality provides a lower bound to the objective function of the primal problem (or the original problem). In this article, we formulate and investigate a Wolfe type duality model for linear optimization problems with equilibrium constraints. Firstly, we propose the Wolfe type duality model and give an example to illustrate the given dual model. Secondly, we establish the weak duality and strong duality theorems for a pair of the primal problem (LOPEC) and the Wolfe type dual problem (DWLOPEC). Finally, we present an example to illustrate the strong duality result in the paper.
Keywords
Download Citation
Endnote/Zotero/Mendeley (RIS)BibTeX
-
[1] R. I. Bot, S. -M. Grad (2010). Wolfe duality and Mond-Weir duality via perturbations. Nonlinear Anal. Theory Methods Appl., 73(2), 374-384.
[2] S. Dempe, A. B. Zemkoho (2012). Bilevel road pricing: Theoretical analysis and optimality conditions. Ann. Oper. Research, 196, 223-240.
[3] Z. Q. Luo, J. S. Pang, D. Ralph (1996). Mathematical problems with equilibrium constraints. Cambridge University Press, Cambridge.
[4] P. Wolfe (1961). A duality theorem for nonlinear programming. Q. J. Appl. Math, 19, 239-244.
[5] J. J. Ye (2005). Necessary and sufficient optimality conditions for mathematical program with equilibrium constraints. J. Math. Anal. Appl., 307, 350-369.
[6] R. T. Rockafellar (1970). Convex Analysis. Princeton Univ. Press, Princeton.
[7] Phí Mạnh Ban (2015). Quy hoạch tuyến tính, NXB Đại học Sư phạm.