M. A. López-Cerdá
We present some characterizations of the subdifferential of the supremum function of finitely and infinitely indexed families of convex functions. They use similar conditions as those of Moreau-Rockafellar's sum rule, involving either the relative interior of the domains in the finite-dimensional setting, or the continuity of the data functions in infinite dimensions. The resulting formulas are given in terms of the exact subdifferential of the data functions at the reference point, and not at nearby points. We also derive new Fritz-John and KKT-type optimality conditions for (semi-infinite) convex optimization, dropping the standard continuity assumptions.
Palabras clave / Keywords: supremum function, convex functions, subdifferential calculus rules, qualification conditions
Programado
Sesión GT11-2: Optimización Continua-2 (OPTIMIZACIÓN-2). Organizador: Juan Parra López
29 de mayo de 2018 10:30
Sala 6
