Geodesic
Semi-algebraic Semicontinuity Of Vector-valued Maps And Applications
Minimax theory and its applications, Tome 10 (2025) no. 1
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T his paper proposes concepts of semicontinuity of vector-valued maps in the sense of “semi-algebra”, that is, the image spaces are not endowed with any particular topology. Properties as well as characterizations of these concepts are discussed. We use these results together with new concepts of generalized quasiconvexity of vector-valued map to study existence conditions and the (semi)continuity of solution maps to vector equilibrium problems. Wellposedness under perturbations for vector equilibrium problems with equilibrium constraints is also presented.
Mots-clés : Semicontinuity, algebraic interior, vector equilibrium problem, existence of solution, generalized quasiconvexity 
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     author = {L.Q. Anh and H.M. Linh and T.N. Tam},
     title = {Semi-algebraic {Semicontinuity} {Of} {Vector-valued} {Maps} {And} {Applications}},
     journal = {Minimax theory and its applications},
     year = {2025},
     volume = {10},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/MTA_2025_10_1_a3/}
}
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L.Q. Anh; H.M. Linh; T.N. Tam. Semi-algebraic Semicontinuity Of Vector-valued Maps And Applications. Minimax theory and its applications, Tome 10 (2025) no. 1. http://geodesic.mathdoc.fr/item/MTA_2025_10_1_a3/