Generalized Minimizers of Convex Integral Functionals and Pythagorean Identities

Integral functionals based on convex normal integrands are minimized subject to finitely many moment constraints. The effective domain of the value function is described by a modification of the concept of convex core. The minimization is viewed as a primal problem and studied together with a dual one in the framework of convex duality. The minimizers and generalized minimizers are explicitly described whenever the primal value is finite, assuming a dual constraint qualification but not the primal constraint qualification. A generalized Pythagorean identity is presented using Bregman distance and a correction term. 1 The problem Proc. Geometric Science of Information 2013, Springer LNCS 8085, 302–307. This contribution addresses minimization of integral functionals