Báo cáo hóa học: " Research Article ε-Optimal Solutions in Nonconvex Semi-Infinite Programs with Support Functions"

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 ε-Optimal Solutions in Nonconvex Semi-Infinite Programs with Support Functions | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011 Article ID 175327 13 pages doi 2011 175327 Research Article -Optimal Solutions in Nonconvex Semi-Infinite Programs with Support Functions Do Sang Kim1 and Ta Quang Son2 1 Department of Applied Mathematics Pukyong National University Busan 608-737 Republic of Korea 2 Department of Natural Sciences Nhatrang College of Education 1 Nguyen Chanh Nhatrang Vietnam Correspondence should be addressed to Do Sang Kim dskim@ Received 6 December 2010 Accepted 29 December 2010 Academic Editor Jen Chih Yao Copyright 2011 D. S. Kim and T. Q. Son. 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. Approximate optimality conditions for a class of nonconvex semi-infinite programs involving support functions are given. The objective function and the constraint functions are locally Lipschitz functions on R . By using a Karush-Kuhn-Tucker KKT condition we deduce a necessary optimality condition for local approximate solutions. Then generalized KKT conditions for the problems are proposed. Based on properties of e-semiconvexity and semiconvexity applied to locally Lipschitz functions and generalized KKT conditions we establish sufficient optimality conditions for another kind of local approximate solutions of the problems. Obtained results in case of nonconvex semi-infinite programs and nonconvex infinite programs are discussed. 1. Introduction There were several papers concerning approximate solutions of convex nonconvex problems published over years such as 1-10 . Recently optimization problems which have a number of infinite constraints were considered in several papers such as 9-15 . In particular approximate optimality conditions of nonconvex problems with infinite constraints were investigated in 9 10 . On the other side finite

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