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July  2007, 3(3): 503-517. doi: 10.3934/jimo.2007.3.503

Semilocally prequasi-invex functions and characterizations

Jin-bao Jian 1, , Hua-qin Pan 1, and  Han-jun Zeng 1,

1. 

College of Mathematics and Information Science, Guangxi University, 530004, Nanning, P.R., China, China, China

Received  August 2006 Revised  January 2007 Published  July 2007

In this paper, based on semilocal convexity, invexity and prequasi-invexity, a new kind of generalized convexity called (strictly/ semistrictly) semilocally prequasi-invex functions is presented, and some of their basic characterizations are discussed. Then, several necessary and sufficient conditions for the proposed generalized convexity are established. Finally, some important properties of the optimal solutions to the associated generalized convex optimization problems are discussed.
Keywords: locally invex set, semilocally prequasi-invex functions, prequasi-invex functions, generalized convexity..
Mathematics Subject Classification: 90C30, 90C53, 49M37, 65K10, 65K0.
Citation: Jin-bao Jian, Hua-qin Pan, Han-jun Zeng. Semilocally prequasi-invex functions and characterizations. Journal of Industrial & Management Optimization, 2007, 3 (3) : 503-517. doi: 10.3934/jimo.2007.3.503
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