A Class of Semilocal ?? -Preinvex Functions and Its Applications in Nonlinear Programming

Hehua Jiao, Sanyang Liu and Xinying Pai

Journal of Applied Mathematics, 2012, vol. 2012, 1-19

Abstract:

A kind of generalized convex set, called as local star-shaped ?? -invex set with respect to ?? , is presented, and some of its important characterizations are derived. Based on this concept, a new class of functions, named as semilocal ?? -preinvex functions, which is a generalization of semi- ?? -preinvex functions and semilocal ?? -convex functions, is introduced. Simultaneously, some of its basic properties are discussed. Furthermore, as its applications, some optimality conditions and duality results are established for a nonlinear programming.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:629194

DOI: 10.1155/2012/629194

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