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Strong Duality for Generalized Convex Optimization Problems

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Abstract

In this paper, strong duality for nearly-convex optimization problems is established. Three kinds of conjugate dual problems are associated to the primal optimization problem: the Lagrange dual, Fenchel dual, and Fenchel-Lagrange dual problems. The main result shows that, under suitable conditions, the optimal objective values of these four problems coincide.

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Author information

Authors and Affiliations

  1. Assistant Professor, Faculty of Mathematics, Chemnitz University of Technology, Chemnitz, Germany

    R. I. Boţ

  2. Associate Professor, Faculty of Mathematics and Computer Science, Babeş – Bolyai University, Cluj-Napoca, Romania

    G. Kassay

  3. Professor, Faculty of Mathematics, Chemnitz University of Technology, Chemnitz, Germany

    G. Wanka

Authors
  1. R. I. Boţ
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  2. G. Kassay
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  3. G. Wanka
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Additional information

The first author was supported in part by Gottlieb Daimler and Karl Benz Stiftung 02-48/99.

This research has been performed while the second author visited Chemnitz University of Technology under DAAD (Deutscher Akademischer Austauschdienst) Grant A/02/12866.

Communicated by T. Rapcsák

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Boţ, R.I., Kassay, G. & Wanka, G. Strong Duality for Generalized Convex Optimization Problems. J Optim Theory Appl 127, 45–70 (2005). https://doi.org/10.1007/s10957-005-6392-5

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  • DOI: https://doi.org/10.1007/s10957-005-6392-5

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