Stability and well-posedness for parametric quasivariational inequality problem

Monika Mehta, Guneet Bhatia () and Ruchi Kaur
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Monika Mehta: University of Delhi
Guneet Bhatia: University of Delhi
Ruchi Kaur: University of Delhi

Mathematical Methods of Operations Research, 2025, vol. 101, issue 3, No 6, 529-548

Abstract: Abstract In this paper, we perform a general analysis of stability and well-posedness for a parametric quasivariational inequality problem. Various sufficient conditions ensuring stability, in terms of semicontinuity and closedness of the parametric solution set map are established. Metric characterizations of Levitin–Polyak (LP) well-posedness via approximate solutions sets are also derived. A key result characterizing LP well-posedness in terms of the upper semicontinuity of the approximate solution set has been proved.

Keywords: Quasivariational inequality; Set-valued map; Stability; Well-posedness; Lower semicontinuity; Upper semicontinuity; 49J40; 49K40; 90C31; 54C60 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00186-025-00897-0

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