Nondifferentiable multiobjective programming under generalized d-univexity |
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| Institution: | 1. Department of Mathematics, Statistics and Computer Science, College of Basic Sciences and Humanities, Govind Ballabh Pant University of Agriculture and Technology, Pantnagar 263 145, India;2. Institute of Systems Science, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100080, China;3. Department of Management Sciences, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong;1. University of Ni?, Faculty of Sciences and Mathematics, Vi?egradska 33, 18000 Ni?, Serbia;2. University of Novi Sad, Faculty of Science, Trg D. Obradovi?a 4, 21000 Novi Sad, Serbia |
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| Abstract: | In this paper, we are concerned with a nondifferentiable multiobjective programming problem with inequality constraints. We introduce four new classes of generalized convex functions by combining the concepts of weak strictly pseudoinvex, strong pseudoinvex, weak quasi invex, weak pseudoinvex and strong quasi invex functions in Aghezzaf and Hachimi Numer. Funct. Anal. Optim. 22 (2001) 775], d-invex functions in Antczak Europ. J. Oper. Res. 137 (2002) 28] and univex functions in Bector et al. Univex functions and univex nonlinear programming, Proc. Admin. Sci. Assoc. Canada, 1992, p. 115]. By utilizing the new concepts, we derive a Karush–Kuhn–Tucker sufficient optimality condition and establish Mond–Weir type and general Mond–Weir type duality results for the nondifferentiable multiobjective programming problem. |
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