Quasi-relative Interiors for Graphs of Convex Set-valued Mappings
B. S. Mordukhovich: Research of this author was partly supported by the USA National Science Foundation under Grants DMS-1512846 and DMS-1808978, by the USA Air Force Office of Scientific Research Grant #15RT04, and by the Australian Research Council under Discovery Project DP-190100555. N. M. Nam: Research of this author was partly supported by the USA National Science Foundation under Grant DMS-1716057.
This paper aims at providing further studies of the notion of quasi-relative interior for convex sets. We obtain new formulas for representing quasi-relative interiors of convex graphs of set-valued mappings and for convex epigraphs of extended-real-valued functions defined on locally convex topological vector spaces. We also show that the role, which this notion plays in infinite dimensions and the results obtained in this vein, are similar to those involving relative interior in finite-dimensional spaces.
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Van Cuong, D., Mordukhovich, B.S. & Nam, N.M. Quasi-relative interiors for graphs of convex set-valued mappings. Optim Lett 15, 933–952 (2021). https://doi.org/10.1007/s11590-019-01447-4