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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 Weak ψ-Sharp Minima in Vector Optimization Problems | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 154598 10 pages doi 10.1155 2010 154598 Research Article Weak y-Sharp Minima in Vector Optimization Problems S. Xu and S. J. Li College of Mathematics and Statistics Chongqing University Chongqing 400030 China Correspondence should be addressed to S. Xu xxushu@126.com Received 23 April 2010 Revised 15 July 2010 Accepted 13 August 2010 Academic Editor N. J. Huang Copyright 2010 S. Xu 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. We present a sufficient and necessary condition for weak y-sharp minima in infinite-dimensional spaces. Moreover we develop the characterization of weak y-sharp minima by virtue of a nonlinear scalarization function. 1. Introduction The notion of a weak sharp minimum in general mathematical program problems was first introduced by Ferris in 1 . It is an extension of sharp minimum in 2 . Weak sharp minima play important roles in the sensitivity analysis 3 4 and convergence analysis of a wide range of optimization algorithms 5 . Recently the study of weak sharp solution set covers real-valued optimization problems 5-8 and piecewise linear multiobjective optimization problems 9-11 . Most recently Bednarczuk 12 defined weak sharp minima of order m for vectorvalued mappings under an assumption that the order cone is closed convex and pointed and used the concept to prove upper Holderness and Holder calmness of the solution set-valued mappings for a parametric vector optimization problem. In 13 Bednarczuk discussed the weak sharp solution set to vector optimization problems and presented some properties in terms of well-posedness of vector optimization problems. In 14 Studniarski gave the definition of weak y-sharp local Pareto minimum in vector optimization problems under the .