Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : Equivalent properties of global weak sharp minima with applications | Zhou and Xu Journal of Inequalities and Applications 2011 2011 137 http content 2011 1 137 3 Journal of Inequalities and Applications a SpringerOpen Journal RESEARCH Open Access Equivalent properties of global weak sharp minima with applications Jinchuan Zhou 1 and Xiuhua Xu2 Correspondence jinchuanzhou@ department of Mathematics School of Science Shandong University of Technology Zibo 255049 China Full list of author information is available at the end of the article Springer Abstract In this paper we study the concept of weak sharp minima using two different approaches. One is transforming weak sharp minima to an optimization problem another is using conjugate functions. This enable us to obtain some new characterizations for weak sharp minima. Mathematics Subject Classification 2000 90C30 90C26. Keywords weak sharp minima error bounds conjugate functions 1 Introduction The notion of weak sharp minima plays an important role in the analysis of the perturbation behavior of certain classes of optimization problems as well as in the convergence analysis of algorithms. Of particular note in this fields is the paper by Burke and Ferris 1 which gave an extensive exposition of the notation and its impacted on convex programming and convergence analysis. Since then this notion was extensively studied by many authors for example necessary or sufficient conditions of weak sharp minima for nonconvex programming 2 3 and necessary and sufficient conditions of local weak sharp minima for sup-type or lower-C1 functions 4 5 . Recent development of weak sharp minima and its related to other issues can be found in 5-8 . A closed set Sc Rn is said to be a set of weak sharp minima for a function f Rn R relative to a closed set S Rn with Sc S if there is an a 0 such that f x f y adist x S Vx e Sandy e S 1 1 where dist x S denotes the Euclidean distance from x to S . dist x S inf x - y II y e S . An ordinary way to deal with weak
