<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Let <italic>X</italic> be a Banach space while (<italic>Y</italic>,⪯) a Banach lattice. We consider the class of “upper separated” set-valued functions <italic>F</italic> : <italic>X</italic> → 2<sup><italic>Y</italic></sup> and investigate the problem of the existence of order-convex selections of <italic>F</italic>. 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.</p></abstract>

Let X be a Banach space while (Y,⪯) a Banach lattice. We consider the class of “upper separated” set-valued functions F : X → 2Y 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.

Upper separated multifunctions in deterministic and stochastic optimal control

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Upper separated multifunctions in deterministic and stochastic optimal control"}

Let X be a Banach space while (Y,⪯) a Banach lattice. We consider the class of “upper separated” set-valued functions F : X → 2Y and investigate the problem of...

Upper separated multifunctions in deterministic and stochastic optimal control

Article Category: Regular Articles

Published Online: Nov 20, 2017

Page range: 479 - 484

Received: Jun 08, 2017

Accepted: Nov 20, 2017

DOI: https://doi.org/10.21042/AMNS.2017.2.00039

Keywords
Banach lattice, upper separated multifunction, convex selection, differential inclusion, optimal control

© 2017 Jerzy Motyl, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Upper separated multifunctions in deterministic and stochastic optimal control

Article Category: Regular Articles

Published Online: Nov 20, 2017

Page range: 479 - 484

Received: Jun 08, 2017

Accepted: Nov 20, 2017

DOI: https://doi.org/10.21042/AMNS.2017.2.00039

KeywordsBanach lattice, upper separated multifunction, convex selection, differential inclusion, optimal control

© 2017 Jerzy Motyl, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Banach lattice, upper separated multifunction, convex selection, differential inclusion, optimal control