About Semicontinuity of Set-valued Maps and Stability of Quasivariational Inclusions
Lâm Quốc Anh, Phan Quốc Khánh, Đinh Ngọc Quý · Set-Valued and Variational Analysis · 2014
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.