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

Author

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  • Hehua Jiao
  • Sanyang Liu
  • Xinying Pai

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.

Suggested Citation

  • Hehua Jiao & Sanyang Liu & Xinying Pai, 2012. "A Class of Semilocal ?? -Preinvex Functions and Its Applications in Nonlinear Programming," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-19, February.
    • Handle: RePEc:hin:jnljam:629194
    DOI: 10.1155/2012/629194
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