 Название: Design of Distributed and Robust Optimization Algorithms: A Systems Theoretic Approach
Автор: Simon Michalowsky
Издательство: Logos Verlag Berlin GmbH
Год: 2020
Страниц: 169
Язык: английский
Формат: pdf (true)
Размер: 10.1 MB
Optimization algorithms are the backbone of many modern technologies. In this thesis, we address the analysis and design of optimization algorithms from a systems theoretic viewpoint. By properly recasting the algorithm design as a controller synthesis problem, we derive methods that enable a systematic design of tailored optimization algorithms. We consider two specific classes of optimization algorithms: (i) distributed, and (ii) robust optimization algorithms.
Concerning (i), we utilize ideas from geometric control in an innovative fashion to derive a novel methodology that enables the design of distributed optimization algorithms under minimal assumptions on the graph topology and the structure of the optimization problem. Concerning (ii), we employ robust control techniques to establish a framework for the analysis of existing algorithms as well as the design of novel robust optimization algorithms with specified guarantees.
Optimization plays an important role in many fields of applications and is the backbone of a multitude of modern technologies such as real-time control, Machine Learning or data analytics. Having reliable, fast and flexible optimization algorithms available hence is of key importance. Over the last decades, a variety of optimization algorithms applicable in different situations have been developed and proven themselves in real-world applications. However, the technological progress often requires the adaptation to novel challenges that existing algorithms cannot handle appropriately, hence necessitating the development of tailored algorithms. Though, it is fair to say that the design of new algorithms, but also their analysis, still is more art than science based on experience, expert knowledge and good ideas. A systematic framework to analyze and modify existing or design novel algorithms adapted to different situations is not available yet. On the other hand, many optimization algorithms are, in essence, dynamical systems having an equilibrium characterized by the solutions of a class of optimization problems. Systems and control theory provides a quite mature set of tools for analyzing the convergence and stability properties of equilibria as well as for designing controllers that stabilize a given equilibrium. While the apparentrelation between these two areas of research is not a new discovery, its full potential has not been exploited yet.
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