Open AccessUpper separated multifunctions in deterministic and stochastic optimal control
Author(s) -
Jerzy Motyl
Publication year - 2017
Publication title -
applied mathematics and nonlinear sciences
Language(s) - English
Resource type - Journals
ISSN - 2444-8656
DOI - 10.21042/amns.2017.2.00039
Subject(s) - mathematics , banach space , regular polygon , differential inclusion , upper and lower bounds , class (philosophy) , lattice (music) , type (biology) , stochastic control , pure mathematics , combinatorics , mathematical optimization , mathematical analysis , optimal control , computer science , physics , geometry , artificial intelligence , acoustics , ecology , biology
Let X be a Banach space while ( Y ,⪯) a Banach lattice. We consider the class of “upper separated” set-valued functions F : X → 2 Y and investigate the problem of the existence of order-convex selections of F . First, we present results on the existence of the Carathéodory-convex type selections of upper separated multifunctions and apply them to investigation of the existence of solutions of differential and stochastic inclusions. We will discuss the applicability of obtained selection results to some deterministic and stochastic optimal control problems.