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Advances in Global Optimization pp 315–323Cite as

A Canonical Duality Approach for the Solution of Affine Quasi-Variational Inequalities

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 95))

Abstract

We apply a sequential dual canonical transformation on the global optimization problem resulting from the reformulation of the Karush–Kuhn–Tucker conditions of affine quasi-variational inequalities (QVIs) using the Fischer-Burmeister complementarity function. Canonical duality is generally able to provide conditions for a critical point of the dual formulation to be the corresponding point of a global optimum of the original problem. By studying the new dual formulation it is possible to obtain properties that are not evident from the original one and that can be useful to develop new methods for the solution of (not necessarily affine) QVIs. The resulting formulation is canonically dual to the original in the sense that there is no duality gap between critical points of the original problem and those of the dual one.

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Authors and Affiliations

  1. Department of Computer Control and Management Engineering, Sapienza University of Rome, via Ariosto 25, 00185, Roma, Italy

    Vittorio Latorre & Simone Sagratella

Authors
  1. Vittorio Latorre
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  2. Simone Sagratella
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Correspondence to Vittorio Latorre .

Editor information

Editors and Affiliations

  1. School of Science, Information Technology and Engineering, Federation University Australia, Ballarat, Victoria, Australia

    David Gao

  2. School Science, Inform., Tech. & Engg., Federation University Australia, Ballarat, Victoria, Australia

    Ning Ruan

  3. Dept. of Mathematical Sciences, Tsinghua University, Beijing, China

    Wenxun Xing

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Latorre, V., Sagratella, S. (2015). A Canonical Duality Approach for the Solution of Affine Quasi-Variational Inequalities. In: Gao, D., Ruan, N., Xing, W. (eds) Advances in Global Optimization. Springer Proceedings in Mathematics & Statistics, vol 95. Springer, Cham. https://doi.org/10.1007/978-3-319-08377-3_31

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