TAILIEUCHUNG - Báo cáo hóa học: " Characterizations of the solution sets of pseudoinvex programs and variational inequalities"

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: Characterizations of the solution sets of pseudoinvex programs and variational inequalities | Liu et al. Journal of Inequalities and Applications 2011 2011 32 http content 2011 1 32 Journal of Inequalities and Applications a SpringerOpen Journal RESEARCH Open Access Characterizations of the solution sets of pseudoinvex programs and variational inequalities Caiping Liu1 Xinmin Yang2 and Heungwing Lee3 Correspondence xmyang@cqnu. 2Department of Mathematics Chongqing Normal University Chongqing 400047 China Full list of author information is available at the end of the article SpringerOpen0 Abstract A new concept of nondifferentiable pseudoinvex functions is introduced. Based on the basic properties of this class of pseudoinvex functions several new and simple characterizations of the solution sets for nondifferentiable pseudoinvex programs are given. Our results are extension and improvement of some results obtained by Mangasarian Oper. Res. Lett. 7 21-26 1988 Jeyakumar and Yang J. Optim. Theory Appl. 87 747-755 1995 Ansari et al. Riv. Mat. Sci. Econ. Soc. 22 31-39 1999 Yang J. Optim. Theory Appl. 140 537-542 2009 . The concepts of Stampacchia-type variational-like inequalities and Minty-type variational-like inequalities defined by upper Dini directional derivative are introduced. The relationships between the variational-like inequalities and the nondifferentiable pseudoinvex optimization problems are established. And the characterizations of the solution sets for the Stampacchia-type variational-like inequalities and Minty-type variational-like inequalities are derived. Keywords Solution sets Pseudoinvex programs Variational-like inequalities Optimization problem Dini directional derivatives 1 Introduction Characterizations and properties of the solution sets are useful for understanding the behavior of solution methods for programs that have multiple optimal solutions. Man-gasarian 1 presented several characterizations of the solution sets for differentiable convex programs and applied them to study .

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