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Journal of Control Science and Engineering
Volume 2011, Article ID 127208, 9 pages
Research Article

Higher-Order Generalized Invexity in Control Problems

Department of Mathematics, Indian Institute of Technology, Kharagpur-721302, India

Received 13 December 2010; Accepted 30 March 2011

Academic Editor: Onur Toker

Copyright © 2011 S. K. Padhan and C. Nahak. 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.


We introduce a higher-order duality (Mangasarian type and Mond-Weir type) for the control problem. Under the higher-order generalized invexity assumptions on the functions that compose the primal problems, higher-order duality results (weak duality, strong duality, and converse duality) are derived for these pair of problems. Also, we establish few examples in support of our investigation.