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Open Access

Optimality and Duality in Nonsmooth Multiobjective Optimization Involving V-Type I Invex Functions

Journal of Inequalities and Applications20102010:898626

Received: 4 June 2010

Accepted: 26 September 2010

Published: 14 October 2010


A new class of generalized V-type I invex functions is introduced for nonsmooth multiobjective programming problem. Based upon these generalized invex functions, we establish sufficient optimality conditions for a feasible point to be an efficient or a weakly efficient solution. Weak, strong, and strict converse duality theorems are proved for Mond-Weir type dual program in order to relate the weakly efficient solutions of primal and dual programs.


Programming ProblemMultiobjective OptimizationEfficient SolutionFeasible PointDuality Theorem

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Authors’ Affiliations

Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
Department of Mathematical Sciences, Florida Institute of Techynology, Melbourne, USA
Department of Mathematics, Aligarh Muslim University, Aligarh, India
Department of Mathematics, Faculty of Applied Sciences, Integral University, Lucknow, India
Department of Applied Mathematics, Birla Institute of Technology, Mesra, India


© Ravi P. Agarwal et al. 2010

This article is published under license to BioMed Central Ltd. 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.