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

Author

Listed:
  • Hehua Jiao
  • Sanyang Liu
  • Xinying Pai

Abstract

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.

Suggested Citation

  • Hehua Jiao & Sanyang Liu & Xinying Pai, 2012. "A Class of Semilocal E‐Preinvex Functions and Its Applications in Nonlinear Programming," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:629194
    DOI: 10.1155/2012/629194
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    References listed on IDEAS

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    1. E. A. Youness, 1999. "E-Convex Sets, E-Convex Functions, and E-Convex Programming," Journal of Optimization Theory and Applications, Springer, vol. 102(2), pages 439-450, August.
    2. Kaul, R. N. & Kaur, Surjeet, 1982. "Generalizations of convex and related functions," European Journal of Operational Research, Elsevier, vol. 9(4), pages 369-377, April.
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