A. Hantoute, F. Flores-Bazán
Convex representatives are proposed for the value function of an infinite dimensional constrained nonconvex variational problem. All the involved variables in this problem take their values in (possibly of infinite dimension, not necessarily separable or Banach) normed spaces, while the associated measure can be any σ-finite, nonnegative and nonatomic measure. This in particular shows that the closure hull of the (possibly, nonconvex) value function is always convex, as long as the sense of the integral within the vector-valued functional constraint is given and the type of the closure is appropriately determined. Correspondingly, similar convexity properties for the Aumann integral in general normed spaces of infinite dimension are established. Applications are given in a fairly general positively homogeneous framework.
Palabras clave: Value function, nonconvex optimization, Bochner, Pettis and Gelfand integrals, convex representative functions, positively homogeneous problems.
Programado
GT11 Optimización Continua II
9 de junio de 2022 12:00
A12
