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On a Smooth Dual Gap Function for a Class of Quasi-Variational Inequalities

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Listed:
  • Nadja Harms

    (University of Würzburg)

  • Tim Hoheisel

    (University of Würzburg)

  • Christian Kanzow

    (University of Würzburg)

Abstract

A well-known technique for the solution of quasi-variational inequalities (QVIs) consists in the reformulation of this problem as a constrained or unconstrained optimization problem by means of so-called gap functions. In contrast to standard variational inequalities, however, these gap functions turn out to be nonsmooth in general. Here, it is shown that one can obtain an unconstrained optimization reformulation of a class of QVIs with affine operator by using a continuously differentiable dual gap function. This extends an idea from Dietrich (J. Math. Anal. Appl. 235:380–393 [24]). Some numerical results illustrate the practical behavior of this dual gap function approach.

Suggested Citation

  • Nadja Harms & Tim Hoheisel & Christian Kanzow, 2014. "On a Smooth Dual Gap Function for a Class of Quasi-Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 163(2), pages 413-438, November.
    • Handle: RePEc:spr:joptap:v:163:y:2014:i:2:d:10.1007_s10957-014-0536-4
    DOI: 10.1007/s10957-014-0536-4
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    References listed on IDEAS

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