Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/6521
Title: Characterizations of the solution sets of pseudoinvex programs and variational inequalities
Authors: Liu, C
Yang, X
Lee, HWJ 
Keywords: Dini directional derivatives
Optimization problem
Pseudoinvex programs
Solution sets
Variational-like inequalities
Issue Date: 17-Aug-2011
Publisher: Springer
Source: Journal of inequalities and applications, 17 Aug. 2011, 2011:32, p. 1-13 How to cite?
Journal: Journal of inequalities and applications 
Abstract: A new concept of nondifferentiable pseudoinvex functions is introduced. Based on the basic properties of this class of pseudoinvex functions, several new and simple characterizations of the solution sets for nondifferentiable pseudoinvex programs are given. Our results are extension and improvement of some results obtained by Mangasarian (Oper. Res. Lett., 7, 21-26, 1988), Jeyakumar and Yang (J. Optim. Theory Appl., 87, 747-755, 1995), Ansari et al. (Riv. Mat. Sci. Econ. Soc., 22, 31-39, 1999), Yang (J. Optim. Theory Appl., 140, 537-542, 2009). The concepts of Stampacchia-type variational-like inequalities and Minty-type variational-like inequalities, defined by upper Dini directional derivative, are introduced. The relationships between the variational-like inequalities and the nondifferentiable pseudoinvex optimization problems are established. And, the characterizations of the solution sets for the Stampacchia-type variational-like inequalities and Minty-type variational-like inequalities are derived.
URI: http://hdl.handle.net/10397/6521
ISSN: 1029-242X
DOI: 10.1186/1029-242X-2011-32
Rights: © 2011 Liu et al; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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