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Levitin–Polyak well-posedness for parametric quasivariational inequality problem of the Minty type

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Abstract

In this paper, we introduce the notions of Levitin–Polyak (LP) well-posedness and Levitin–Polyak well-posedness in the generalized sense, for a parametric quasivariational inequality problem of the Minty type. Metric characterizations of LP well-posedness and generalized LP well-posedness, in terms of the approximate solution sets are presented. A parametric gap function for the quasivariational inequality problem is introduced and an equivalence relation between LP well-posedness of the parametric quasivariational inequality problem and that of the related optimization problem is obtained.

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Authors and Affiliations

  1. Department of Mathematics, University of Delhi South Campus, Benito Jaurez Road, New Delhi, 110021, India

    C. S. Lalitha

  2. Department of Mathematics, University of Delhi, Delhi, 110007, India

    Guneet Bhatia

Authors
  1. C. S. Lalitha
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  2. Guneet Bhatia
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Correspondence to C. S. Lalitha.

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Research of C.S. Lalitha is supported by R&D Doctoral Research Programme funds for the university faculty.

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Lalitha, C.S., Bhatia, G. Levitin–Polyak well-posedness for parametric quasivariational inequality problem of the Minty type. Positivity 16, 527–541 (2012). https://doi.org/10.1007/s11117-012-0188-2

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