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Stability Analysis for Parameterized Variational Systems with Implicit Constraints

Set-Valued and Variational Analysis volume 28, pages 167–193 (2020)Cite this article

Abstract

In the paper we provide new conditions ensuring the isolated calmness property and the Aubin property of parameterized variational systems with constraints depending, apart from the parameter, also on the solution itself. Such systems include, e.g., quasi-variational inequalities and implicit complementarity problems. Concerning the Aubin property, possible restrictions imposed on the parameter are also admitted. Throughout the paper, tools from the directional limiting generalized differential calculus are employed enabling us to impose only rather weak (non- restrictive) qualification conditions. Despite the very general problem setting, the resulting conditions are workable as documented by some academic examples.

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Acknowledgements

The research of the first two authors was supported by the Austrian Science Fund (FWF) under grant P29190-N32. The research of the third author was supported by the Grant Agency of the Czech Republic, Project 17-08182S and the Australian Research Council, Project DP160100854.

Funding

Open access funding provided by Austrian Science Fund (FWF).

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Affiliations

  1. Institute of Computational Mathematics, Johannes Kepler University Linz, A-4040, Linz, Austria

    Matúš Benko & Helmut Gfrerer

  2. Institute of Information Theory Automation, Academy of Sciences of the Czech Republic, 18208, Prague, Czech Republic

    Jiří V. Outrata

  3. Centre for Informatics Applied Optimization, Federation University of Australia, POB 663, Ballarat, Vic, 3350, Australia

    Jiří V. Outrata

Authors
  1. Matúš Benko
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  2. Helmut Gfrerer
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  3. Jiří V. Outrata
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Corresponding author

Correspondence to Helmut Gfrerer.

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Benko, M., Gfrerer, H. & Outrata, J.V. Stability Analysis for Parameterized Variational Systems with Implicit Constraints. Set-Valued Var. Anal 28, 167–193 (2020). https://doi.org/10.1007/s11228-019-00516-1

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  • DOI: https://doi.org/10.1007/s11228-019-00516-1

Keywords

  • Parameterized variational system
  • Solution map
  • Aubin property
  • Isolated calmness property

Mathematics Subject Classification (2010)

  • 49J53
  • 90C31
  • 90C46