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

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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.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Hanshan Teachers College, Chaozhou, Guangdong Province, China

    D. H. Yuan (Assistant Professor) & X. L. Liu

  2. Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida, USA

    A. Chinchuluun Graduate Student (Professor)

  3. Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida, USA

    P. M. Pardalos

Authors
  1. D. H. Yuan
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  2. X. L. Liu
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  3. A. Chinchuluun Graduate Student
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  4. P. M. Pardalos
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This research was partially supported by NSF and Air Force grants

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Yuan, D.H., Liu, X.L., Chinchuluun, A. et al. Nondifferentiable Minimax Fractional Programming Problems with (C, α, ρ, d)-Convexity. J Optim Theory Appl 129, 185–199 (2006). https://doi.org/10.1007/s10957-006-9052-5

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  • DOI: https://doi.org/10.1007/s10957-006-9052-5

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