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

Levitin–Polyak well-posedness for parametric quasivariational inequality problem of the Minty type 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

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

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Publisher
Springer Journals
Copyright
Copyright © 2012 by Springer Basel AG
Subject
Mathematics; Operator Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics; Potential Theory; Fourier Analysis
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-012-0188-2
Publisher site
See Article on Publisher Site

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.

Journal

PositivitySpringer Journals

Published: Jun 28, 2012

References

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