Convex programming in optimal control and information theory

TL;DR

This thesis develops computational methods for infinite-dimensional optimization problems in optimal control of Markov decision processes and fundamental information theory problems like channel capacity and entropy maximization.

Contribution

It introduces new computational approaches for infinite-dimensional optimization in optimal control and information theory, addressing MDPs and key information theory problems.

Findings

Effective algorithms for continuous-space MDP control

New methods for channel capacity computation

Entropy maximization under moment constraints

Abstract

The main theme of this thesis is the development of computational methods for classes of infinite-dimensional optimization problems arising in optimal control and information theory. The first part of the thesis is concerned with the optimal control of discrete-time continuous space Markov decision processes (MDP). The second part is centred around two fundamental problems in information theory that can be expressed as optimization problems: the channel capacity problem as well as the entropy maximization subject to moment constraints.