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Diewert-Crouzeix conjugation for general quasiconvex duality and applications

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Abstract

A complicated factor in quasiconvex duality is the appearance of extra parameters. In order to avoid these extra parameters, one often has to restrict the class of quasiconvex functions. In this paper, by using the Diewert-Crouzeix conjugation, we present a duality without an extra parameter for general quasiconvex minimization problem. As an application, we prove a decentralization by prices for the Von Neumann equilibrium problem.

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Authors and Affiliations

  1. Institute of Human and Social Sciences, Tokyo Institute of Technology, Oh-Okayama, Meguro-Ku, Tokyo, Japan

    P. T. Thach (Assistant Professor)

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  1. P. T. Thach
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Communicated by S. Schaible

The author is indebted in Professor S. Schaible and the referees for providing valuable suggestions and corrections in the manuscript, which improved this paper. He also expresses his special thanks to Professor J. P. Crouzeix for helpful comments on the extension of Theorem 2.3 to theR-even quasiconvexity and for supplying Ref. 20, and to Professor H. Konno for valuable comments on the Von Neumann equilibrium.

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Thach, P.T. Diewert-Crouzeix conjugation for general quasiconvex duality and applications. J Optim Theory Appl 86, 719–743 (1995). https://doi.org/10.1007/BF02192166

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