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Semilocal E-convexity and semilocal E-convex programming

Published online by Cambridge University Press:  17 April 2009

Qing-Jie Hu ,
Jin-Bao Jian ,
Hai-Yan Zheng  and
Chun-Ming Tang
Qing-Jie Hu
Affiliation:
Department of Information, Hunan Business College, 410205, Changsha, Peoples Republic of China College of Mathematics and Informatics Science, Guangxi University, Nanning, 530004, Peoples Republic of China
Jin-Bao Jian
Affiliation:
College of Mathematics and Informatics Science, Guangxi University, Nanning, 530004, Peoples Republic of China
Hai-Yan Zheng
Affiliation:
Institute of Applied Mathematics, Hunan University, 410082, Changsha, Peoples Republic of China, e-mail: [email protected]
Chun-Ming Tang
Affiliation:
College of Mathematics and Informatics Science, Guangxi University, Nanning, 530004, Peoples Republic of China
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In this paper, a new type of generalised convexity—semilocal E-convexity is introduced by combining the concepts of the semi-E-convexity in X.S. Chen [J. Math. Anal. Appl. 275(2002), 251–262] and semilocal convexity in G.M. Ewing [SIAM. Rev. 19(1977), 202–220], and some of its basic characters are discussed. By utilising the new concepts, we derive some optimality conditions and establish some duality results for the inequality constrained optimisation problem.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 75 , Issue 1 , February 2007 , pp. 59 - 74
Copyright
Copyright © Australian Mathematical Society 2007

References

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