TAILIEUCHUNG - Báo cáo hóa học: " Non-differentiable multiobjective mixed symmetric duality under generalized convexity"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Non-differentiable multiobjective mixed symmetric duality under generalized convexity | Li and Gao Journal of Inequalities and Applications 2011 2011 23 http content 2011 1 23 Journal of Inequalities and Applications a SpringerOpen Journal RESEARCH Open Access Non-differentiable multiobjective mixed symmetric duality under generalized convexity Jueyou Li and Ying Gao Correspondence lijueyou@163. com Department of Mathematics Chongqing Normal University Chongqing 400047 PR China Abstract The objective of this paper is to obtain a mixed symmetric dual model for a class of non-differentiable multiobjective nonlinear programming problems where each of the objective functions contains a pair of support functions. Weak strong and converse duality theorems are established for the model under some suitable assumptions of generalized convexity. Several special cases are also obtained. MS Classification 90C32 90C46. Keywords symmetric duality non-differentiable nonlinear programming generalized convexity support function 1 Introduction Dorn 1 introduced symmetric duality in nonlinear programming by defining a program and its dual to be symmetric if the dual of the dual is the original problem. The symmetric duality for scalar programming has been studied extensively in the literature one can refer to Dantzig et al. 2 Bazaraa and Goode 3 Devi 4 Mond and Weir 5 6 . Mond and Schechter 7 studied non-differentiable symmetric duality for a class of optimization problems in which the objective functions consist of support functions. Following Mond and Schechter 7 Hou and Yang 8 Yang et al. 9 Mishra et al. 10 and Bector et al. 11 studied symmetric duality for such problems. Weir and Mond 6 presented two models for multiobjective symmetric duality. Several authors such as the ones of 12-14 studied multiobjective second and higher order symmetric duality motivated by Weir and Mond 6 . Very recently Mishra et al. 10 presented a mixed symmetric dual formulation for a non-differentiable nonlinear programming problem. Bector et .

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