Artículos de revistas
Moreau-Rockafellar-type formulas for the subdifferential of the supremum function
Fecha
2019Registro en:
SIAM Journal on Optimization, Volumen 29, Issue 2, 2019, Pages 1106-1130
10526234
10.1137/18M1169370
Autor
Correa, Rafael
Hantoute, Abderrahim
López-Cerdá, Marco A.
Institución
Resumen
We characterize the subdifferential of the supremum function of finitely and infinitely indexed families of convex functions. The main contribution of this paper consists of providing formulas for such a subdifferential under weak continuity assumptions. The resulting formulas are given in terms of the exact subdifferential of the data functions at the reference point, and not at nearby points as in [Valadier, C. R. Math. Acad. Sci. Paris, 268 (1969), pp. 39-42]. We also derive new Fritz John- and KKT-type optimality conditions for semi-infinite convex optimization, omitting the continuity/closedness assumptions in [Dinh et al., ESAIM Control Optim. Calc. Var., 13 (2007), pp. 580-597]. When the family of functions is finite, we use continuity conditions concerning only the active functions, and not all the data functions as in [Rockafellar, Proc. Lond. Math. Soc. (3), 39 (1979), pp. 331-355; Volle, Acta Math. Vietnam., 19 (1994), pp. 137-148].