Convex programming in optimal control and information theory

2017/01/01 by Tobias Sutter
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #Artificial intelligence #Computer science #Control (management) #Convex optimization #Dynamic programming #Entropy (arrow of time) #Entropy maximization #Information theory #Markov Chains and Monte Carlo Methods #Markov decision process #Markov process #Mathematical Approximation and Integration #Mathematical optimization #Mathematics #Maximization #Optimal control #Optimization problem #Principle of maximum entropy #Regular polygon #cs.IT #math.IT #math.OC

paper · pdf · doi:10.3929/ethz-b-000218720

PhD thesis, ETH Zurich

openalex publication_date 2017/01/01 · arxiv created 2017/12/13 · arxiv updated 2017/12/14 · openalex created_date 2017/12/22 · openalex updated_date 2026/08/05

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.

Citations

• Topics in Optimal Transportation
• A Mathematical Theory of Communication
• A general method for numerically simulating the stochastic time evolution of coupled chemical reactions
• The Bernstein polynomial basis: A centennial retrospective
• First-order methods of smooth convex optimization with inexact oracle
• I-Divergence Geometry of Probability Distributions and Minimization Problems
• Stochastic Simulation of Chemical Kinetics
• Smooth minimization of non-smooth functions
• From Infinite to Finite Programs: Explicit Error Bounds with\n Applications to Approximate Dynamic Programming