Abstract
We propose several additional kinds of semi-limits and corresponding notions of semicontinuity of a set-valued map. They can be used additionally to known basic concepts of semicontinuity to have a clearer insight of local behaviors of maps. Then, we investigate semicontinuity properties of solution maps to a general parametric quasivariational inclusion, which is shown to include most of optimization-related problems. Consequences are derived for several particular problems. Our results are new or generalize/improve recent existing ones in the literature.
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Anh, L.Q., Khanh, P.Q. & Quy, D.N. About Semicontinuity of Set-valued Maps and Stability of Quasivariational Inclusions. Set-Valued Var. Anal 22, 533–555 (2014). https://doi.org/10.1007/s11228-014-0276-5
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DOI: https://doi.org/10.1007/s11228-014-0276-5
Keywords
- Semi-limits
- Semicontinuity
- Solution maps
- Quasivariational inclusions
- Quasivariational relation problems
- Quasivariational equilibrium problems