Journal of Applied Mathematics

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

Hehua Jiao, Sanyang Liu, and Xinying Pai

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A kind of generalized convex set, called as local star-shaped E -invex set with respect to η, is presented, and some of its important characterizations are derived. Based on this concept, a new class of functions, named as semilocal E -preinvex functions, which is a generalization of semi- E -preinvex functions and semilocal E -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.

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J. Appl. Math., Volume 2012 (2012), Article ID 629194, 19 pages.

First available in Project Euclid: 14 December 2012

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Jiao, Hehua; Liu, Sanyang; Pai, Xinying. A Class of Semilocal $E$ -Preinvex Functions and Its Applications in Nonlinear Programming. J. Appl. Math. 2012 (2012), Article ID 629194, 19 pages. doi:10.1155/2012/629194.

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