Journal of Applied Mathematics
- J. Appl. Math.
- Volume 2012 (2012), Article ID 629194, 19 pages.
A Class of Semilocal -Preinvex Functions and Its Applications in Nonlinear Programming
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.
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. https://projecteuclid.org/euclid.jam/1355495035