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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: Research Article Second-Order Contingent Derivative of the Perturbation Map in Multiobjective Optimization | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011 Article ID 857520 13 pages doi 10.1155 2011 857520 Research Article Second-Order Contingent Derivative of the Perturbation Map in Multiobjective Optimization Q. L. Wang1 and S. J. Li2 1 College of Sciences Chongqing Jiaotong University Chongqing 400074 China 2 College of Mathematics and Statistics Chongqing University Chongqing 400044 China Correspondence should be addressed to Q. L. Wang wangql97@126.com Received 14 October 2010 Accepted 24 January 2011 Academic Editor Jerzy Jezierski Copyright 2011 Q. L. Wang and S. J. Li. 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. Some relationships between the second-order contingent derivative of a set-valued map and its profile map are obtained. By virtue of the second-order contingent derivatives of set-valued maps some results concerning sensitivity analysis are obtained in multiobjective optimization. Several examples are provided to show the results obtained. 1. Introduction In this paper we consider a family of parametrized multiobjective optimization problems PVOP min f u x fu x f2M . fmM 1.1 s.t. u e X x c Rp. Here u is a p-dimensional decision variable x is an n-dimensional parameter vector X is a nonempty set-valued map from Rn to Rp which specifies a feasible decision set and f is an objective map from Rp X Rn to Rm where m n p are positive integers. The norms of all finite dimensional spaces are denoted by II . C is a closed convex pointed cone with nonempty interior in Rm. The cone C induces a partial order C on Rm that is the relation C is defined by y C y y - y e C y y e R. 1.2 2 Fixed Point Theory and Applications We use the following notion. For any y y e Rm y C y y - y e int C. 1.3 Based on these notations we can define the following two sets for a set M in Rm i y0 e
