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Conjugate maps and duality in multiobjective optimization

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Abstract

This paper considers duality in convex vector optimization. A vector optimization problem requires one to find all the efficient points of the attainable value set for given multiple objective functions. Embedding the primal problem into a family of perturbed problems enables one to define a dual problem in terms of the conjugate map of the perturbed objective function. Every solution of the stable primal problem is associated with a certain solution of the dual problem, which is characterized as a subgradient of the perturbed efficient value map. This pair of solutions also provides a saddle point of the Lagrangian map.

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Authors and Affiliations

  1. Department of Mechanical Engineering II, Faculty of Engineering, Tohoku University, Sendai, Japan

    T. Tanino (Associate Professor)

  2. Department of Applied Mathematics and Physics, Faculty of Engineering, Kyoto University, Kyoto, Japan

    Y. Sawaragi (Professor)

Authors
  1. T. Tanino
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  2. Y. Sawaragi
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Communicated by G. Leitmann

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Tanino, T., Sawaragi, Y. Conjugate maps and duality in multiobjective optimization. J Optim Theory Appl 31, 473–499 (1980). https://doi.org/10.1007/BF00934473

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  • DOI: https://doi.org/10.1007/BF00934473

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