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Theoretical and numerical investigation of the D-gap function for box constrained variational inequalities

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Abstract

The D-gap function, recently introduced by Peng and further studied by Yamashita et al., allows a smooth unconstrained minimization reformulation of the general variational inequality problem. This paper is concerned with the D-gap function for variational inequality problems over a box or, equivalently, mixed complementarity problems. The purpose of this paper is twofold. First we investigate theoretical properties in depth of the D-gap function, such as the optimality of stationary points, bounded level sets, global error bounds and generalized Hessians. Next we present a nonsmooth Gauss-Newton type algorithm for minimizing the D-gap function, and report extensive numerical results for the whole set of problems in the MCPLIB test problem collection.

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Authors and Affiliations

  1. Institute of Applied Mathematics, University of Hamburg, Bundesstrasse 55, D-20146, Hamburg, Germany

    Christian Kanzow

  2. Department of Applied Mathematics and Physics, Graduate School of Engineering, Kyoto University, 606-01, Kyoto, Japan

    Masao Fukushima

Authors
  1. Christian Kanzow
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  2. Masao Fukushima
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Correspondence to Christian Kanzow.

Additional information

The work of this author was supported in part by the Scientific Research Grant-in-Aid from the Ministry of Education, Science, Sports and Culture, Japan.

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Kanzow, C., Fukushima, M. Theoretical and numerical investigation of the D-gap function for box constrained variational inequalities. Mathematical Programming 83, 55–87 (1998). https://doi.org/10.1007/BF02680550

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  • DOI: https://doi.org/10.1007/BF02680550

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