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 Generalized Levitin-Polyak Well-Posedness of Vector Equilibrium Problems | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 684304 14 pages doi 2009 684304 Research Article Generalized Levitin-Polyak Well-Posedness of Vector Equilibrium Problems Jian-Wen Peng 1 Yan Wang 1 and Lai-Jun Zhao2 1 College of Mathematics and Computer Science Chongqing Normal University Chongqing 400047 China 2 Management School Shanghai University Shanghai 200444 China Correspondence should be addressed to Lai-Jun Zhao zhao_laijun@ Received 1 July 2009 Revised 19 October 2009 Accepted 18 November 2009 Recommended by Nanjing Jing Huang We study generalized Levitin-Polyak well-posedness of vector equilibrium problems with functional constraints as well as an abstract set constraint. We will introduce several types of generalized Levitin-Polyak well-posedness of vector equilibrium problems and give various criteria and characterizations for these types of generalized Levitin-Polyak well-posedness. Copyright 2009 Jian-Wen Peng et al. 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. 1. Introduction It is well known that the well-posedness is very important for both optimization theory and numerical methods of optimization problems which guarantees that for approximating solution sequences there is a subsequence which converges to a solution. The study of well-posedness originates from Tykhonov 1 in dealing with unconstrained optimization problems. Levitin and Polyak 2 extended the notion to constrained scalar optimization allowing minimizing sequences xn to be outside of the feasible set Xo and requiring d xn X0 the distance from xn to X0 to tend to zero. The Levitin and Polyak well-posedness is generalized in 3 4 for problems with explicit constraint g x e K where g is a continuous map between two metric spaces and K is a closed set. For minimizing .