Semilocally prequasi-invex functions and characterizations

Jin-bao Jian; Hua-qin Pan; Han-jun Zeng

doi:10.3934/jimo.2007.3.503

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2007, Volume 3, Issue 3: 503-517. Doi: 10.3934/jimo.2007.3.503

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Semilocally prequasi-invex functions and characterizations

1.
College of Mathematics and Information Science, Guangxi University, 530004, Nanning, P.R.

Received: July 31, 2006

Revised: December 31, 2006

Published: June 2007

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Abstract

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.

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Mathematics Subject Classification: 90C30, 90C53, 49M37, 65K10, 65K05.

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