Existence of generalized equilibria

✍ Scribed by Bernard Cornet; Marc-Olivier Czarnecki

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 183 KB
• Volume: 44
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/s0362-546x(99)00198-4

✦ Synopsis

belong to R n , we denote (x | y) = n i=1 x i y i , the scalar product of

the sum of the sets X and Y; B(X; r) = X + B(0; r); B(X; r) = X + B(0; r); cl X , the closure of X , int X , the interior of X; bd X = cl X \ int X , the boundary of X; X • = {y ∈ R n |∀x ∈ X; (y | x) ≤ 0}, the negative polar cone of X; co X , the convex hull of X . A map f : X → R is locally Lipschitzian if, for every x ∈ X , there is ¿ 0 and L ¿ 0 such that f(x 1 ) -f(x 2 ) ≤ L x 1 -x 2 for every x 1 and x 2 in B(x; ). If F is a correspondence from X to R n , its graph, denoted by G(F), is deÿned by G(F) = {(x; y) ∈ X × R n | y ∈ F(x)}.