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Journal of Applied Mathematics
Volume 2014, Article ID 453912, 8 pages
http://dx.doi.org/10.1155/2014/453912
Research Article

Strong and Total Lagrange Dualities for Quasiconvex Programming

1College of Mathematics and Statistics, Jishou University, Jishou 416000, China
2Department of Mathematics, China Jiliang University, Hangzhou 310018, China

Received 17 January 2014; Accepted 1 May 2014; Published 22 May 2014

Academic Editor: Ching-Jong Liao

Copyright © 2014 Donghui Fang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the strong and total Lagrange dualities for infinite quasiconvex optimization problems. By using the epigraphs of the -quasi-conjugates and the Greenberg-Pierskalla subdifferential of these functions, we introduce some new constraint qualifications. Under the new constraint qualifications, we provide some necessary and sufficient conditions for infinite quasiconvex optimization problems to have the strong and total Lagrange dualities.