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Equivalence between a generalized fenchel duality theorem and a saddle-point theorem for fractional programs

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Abstract

The convex case of a fractional program is considered. By the aid of a duality theory for mathematical programming involving a maximum and minimum operator, and by defining new operators, we obtain three equivalent duality theorems for three pairs of primal-dual programs. The second and the third one are the saddle-point theorem and a generalized Fenchel duality theorem, respectively.

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Authors and Affiliations

  1. Council for Scientific and Industrial Research, Pretoria, South Africa

    J. Flachs (Research Associate)

  2. Faculty of Industrial Engineering and Management, Technion, Haifa, Israel

    M. A. Pollatschek (Associate Professor)

Authors
  1. J. Flachs
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  2. M. A. Pollatschek
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Communicated by M. Avriel

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Flachs, J., Pollatschek, M.A. Equivalence between a generalized fenchel duality theorem and a saddle-point theorem for fractional programs. J Optim Theory Appl 37, 23–32 (1982). https://doi.org/10.1007/BF00934364

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