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Approximate values for mathematical programs with variational inequality constraints

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Abstract

In general the infimal value of a mathematical program with variational inequality constraints (MPVI) is not stable under perturbations in the sense that the sequence of infimal values for the perturbed programs may not converge to the infimal value of the original problem even in presence of nice data. Thus, for these programs we consider different types of values which approximate the exact value from below or/and from above under or without perturbations.

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Acknowledgements

The authors thanks the Referees and the Editor in charge for their stimulating suggestions that helped to improve the paper.

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Authors and Affiliations

  1. Dipartimento di Matematica e Applicazioni R. Caccioppoli, Università di Napoli Federico II, Via Claudio, 80125, Napoli, Italy

    M. Beatrice Lignola

  2. Dipartimento di Matematica e Statistica & CSEF, Università di Napoli Federico II, Via Cinthia, 80126, Napoli, Italy

    Jacqueline Morgan

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  1. M. Beatrice Lignola
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  2. Jacqueline Morgan
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Correspondence to Jacqueline Morgan.

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Lignola, M.B., Morgan, J. Approximate values for mathematical programs with variational inequality constraints. Comput Optim Appl 53, 485–503 (2012). https://doi.org/10.1007/s10589-012-9470-2

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  • DOI: https://doi.org/10.1007/s10589-012-9470-2

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