Journal of Optimization Theory and Applications

, Volume 129, Issue 1, pp 185–199

Nondifferentiable Minimax Fractional Programming Problems with (C, α, ρ, d)-Convexity

  • D. H. Yuan
  • X. L. Liu
  • A. Chinchuluun
  • P. M. Pardalos
Article

DOI: 10.1007/s10957-006-9052-5

Cite this article as:
Yuan, D.H., Liu, X.L., Chinchuluun, A. et al. J Optim Theory Appl (2006) 129: 185. doi:10.1007/s10957-006-9052-5

Abstract

In this paper, we present necessary optimality conditions for nondifferentiable minimax fractional programming problems. A new concept of generalized convexity, called (C, α, ρ, d)-convexity, is introduced. We establish also sufficient optimality conditions for nondifferentiable minimax fractional programming problems from the viewpoint of the new generalized convexity. When the sufficient conditions are utilized, the corresponding duality theorems are derived for two types of dual programs.

Keywords

Minimax fractional programming problem (C, α, ρ, d)-convexity necessary conditions sufficient conditions duality theory 

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • D. H. Yuan
    • 1
  • X. L. Liu
    • 1
  • A. Chinchuluun
    • 2
  • P. M. Pardalos
    • 3
  1. 1.Department of Mathematics and Computer ScienceHanshan Teachers CollegeChaozhouChina
  2. 2.Department of Industrial and Systems EngineeringUniversity of FloridaGainesvilleUSA
  3. 3.Department of Industrial and Systems EngineeringUniversity of FloridaGainesvilleUSA

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