Optimization Based On Non Commutative Maps

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Optimization Based On Non Commutative Maps

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Author : Jan Feiling
language : en
Publisher: Logos Verlag Berlin GmbH
Release Date : 2022-01-20

Optimization Based On Non Commutative Maps written by Jan Feiling and has been published by Logos Verlag Berlin GmbH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-20 with Mathematics categories.

Powerful optimization algorithms are key ingredients in science and engineering applications. In this thesis, we develop a novel class of discrete-time, derivative-free optimization algorithms relying on gradient approximations based on non-commutative maps–inspired by Lie bracket approximation ideas in control systems. Those maps are defined by function evaluations and applied in such a way that gradient descent steps are approximated, and semi-global convergence guarantees can be given. We supplement our theoretical findings with numerical results. Therein, we provide several algorithm parameter studies and tuning rules, as well as the results of applying our algorithm to challenging benchmarking problems.

Design Of Distributed And Robust Optimization Algorithms A Systems Theoretic Approach

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Author : Simon Michalowsky
language : en
Publisher: Logos Verlag Berlin GmbH
Release Date : 2020-04-17

Design Of Distributed And Robust Optimization Algorithms A Systems Theoretic Approach written by Simon Michalowsky and has been published by Logos Verlag Berlin GmbH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-17 with Technology & Engineering categories.

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.

Determining Input Output Properties Of Linear Time Invariant Systems From Data

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Author : Anne Koch
language : en
Publisher: Logos Verlag Berlin GmbH
Release Date : 2022-02-08

Determining Input Output Properties Of Linear Time Invariant Systems From Data written by Anne Koch and has been published by Logos Verlag Berlin GmbH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-08 with Technology & Engineering categories.

Due to their relevance in systems analysis and controller design, this thesis considers the problem of determining input-output properties of linear time-invariant systems. While obtaining a suitable mathematical model describing the input-output behavior of a dynamical system can be a difficult task, data of the system in form of input-output trajectories is often and increasingly available. This thesis therefore introduces three complementary data-driven analysis methods to determine input-output properties directly from data without deriving a mathematical model first. In particular, the results of this thesis include iterative methods, where data is actively sampled by performing experiments on the unknown system, as well as approaches based on available (offline) data. All these approaches are simple to apply, come with low requirements on the data, and provide rigorous theoretical guarantees. Systems analysis not only provides insights into the system and allows to do controller design with guaranteed stability, but it can also validate a given controller or its closed-loop performance. By developing different methods to determine input-output properties directly from data on the basis of a rigorous mathematical analysis, this thesis contributes to a sound mathematical framework for data-driven systems analysis and control theory.

Mathematical Methods In Systems Optimization And Control

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Author : Harry Dym
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-07-25

Mathematical Methods In Systems Optimization And Control written by Harry Dym and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-25 with Mathematics categories.

This volume is dedicated to Bill Helton on the occasion of his sixty fifth birthday. It contains biographical material, a list of Bill's publications, a detailed survey of Bill's contributions to operator theory, optimization and control and 19 technical articles. Most of the technical articles are expository and should serve as useful introductions to many of the areas which Bill's highly original contributions have helped to shape over the last forty odd years. These include interpolation, Szegö limit theorems, Nehari problems, trace formulas, systems and control theory, convexity, matrix completion problems, linear matrix inequalities and optimization. The book should be useful to graduate students in mathematics and engineering, as well as to faculty and individuals seeking entry level introductions and references to the indicated topics. It can also serve as a supplementary text to numerous courses in pure and applied mathematics and engineering, as well as a source book for seminars.

Handbook On Semidefinite Conic And Polynomial Optimization

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Author : Miguel F. Anjos
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-19

Handbook On Semidefinite Conic And Polynomial Optimization written by Miguel F. Anjos and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-19 with Business & Economics categories.

Semidefinite and conic optimization is a major and thriving research area within the optimization community. Although semidefinite optimization has been studied (under different names) since at least the 1940s, its importance grew immensely during the 1990s after polynomial-time interior-point methods for linear optimization were extended to solve semidefinite optimization problems. Since the beginning of the 21st century, not only has research into semidefinite and conic optimization continued unabated, but also a fruitful interaction has developed with algebraic geometry through the close connections between semidefinite matrices and polynomial optimization. This has brought about important new results and led to an even higher level of research activity. This Handbook on Semidefinite, Conic and Polynomial Optimization provides the reader with a snapshot of the state-of-the-art in the growing and mutually enriching areas of semidefinite optimization, conic optimization, and polynomial optimization. It contains a compendium of the recent research activity that has taken place in these thrilling areas, and will appeal to doctoral students, young graduates, and experienced researchers alike. The Handbook’s thirty-one chapters are organized into four parts: Theory, covering significant theoretical developments as well as the interactions between conic optimization and polynomial optimization; Algorithms, documenting the directions of current algorithmic development; Software, providing an overview of the state-of-the-art; Applications, dealing with the application areas where semidefinite and conic optimization has made a significant impact in recent years.

Foundations Of Free Noncommutative Function Theory

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Author : Dmitry S. Kaliuzhnyi-Verbovetskyi
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-11-19

Foundations Of Free Noncommutative Function Theory written by Dmitry S. Kaliuzhnyi-Verbovetskyi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-19 with Mathematics categories.

In this book the authors develop a theory of free noncommutative functions, in both algebraic and analytic settings. Such functions are defined as mappings from square matrices of all sizes over a module (in particular, a vector space) to square matrices over another module, which respect the size, direct sums, and similarities of matrices. Examples include, but are not limited to, noncommutative polynomials, power series, and rational expressions. Motivation and inspiration for using the theory of free noncommutative functions often comes from free probability. An important application area is "dimensionless" matrix inequalities; these arise, e.g., in various optimization problems of system engineering. Among other related areas are those of polynomial identities in rings, formal languages and finite automata, quasideterminants, noncommutative symmetric functions, operator spaces and operator algebras, and quantum control.

Statistical Inference Via Convex Optimization

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Author : Anatoli Juditsky
language : en
Publisher: Princeton University Press
Release Date : 2020-04-07

Statistical Inference Via Convex Optimization written by Anatoli Juditsky and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-07 with Mathematics categories.

This authoritative book draws on the latest research to explore the interplay of high-dimensional statistics with optimization. Through an accessible analysis of fundamental problems of hypothesis testing and signal recovery, Anatoli Juditsky and Arkadi Nemirovski show how convex optimization theory can be used to devise and analyze near-optimal statistical inferences. Statistical Inference via Convex Optimization is an essential resource for optimization specialists who are new to statistics and its applications, and for data scientists who want to improve their optimization methods. Juditsky and Nemirovski provide the first systematic treatment of the statistical techniques that have arisen from advances in the theory of optimization. They focus on four well-known statistical problems—sparse recovery, hypothesis testing, and recovery from indirect observations of both signals and functions of signals—demonstrating how they can be solved more efficiently as convex optimization problems. The emphasis throughout is on achieving the best possible statistical performance. The construction of inference routines and the quantification of their statistical performance are given by efficient computation rather than by analytical derivation typical of more conventional statistical approaches. In addition to being computation-friendly, the methods described in this book enable practitioners to handle numerous situations too difficult for closed analytical form analysis, such as composite hypothesis testing and signal recovery in inverse problems. Statistical Inference via Convex Optimization features exercises with solutions along with extensive appendixes, making it ideal for use as a graduate text.

Intelligent Computing Optimization

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Author : Pandian Vasant
language : en
Publisher: Springer Nature
Release Date : 2021-12-30

Intelligent Computing Optimization written by Pandian Vasant and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-30 with Technology & Engineering categories.

This book includes the scientific results of the fourth edition of the International Conference on Intelligent Computing and Optimization which took place at December 30–31, 2021, via ZOOM. The conference objective was to celebrate “Compassion and Wisdom” with researchers, scholars, experts and investigators in Intelligent Computing and Optimization worldwide, to share knowledge, experience, innovation—marvelous opportunity for discourse and mutuality by novel research, invention and creativity. This proceedings encloses the original and innovative scientific fields of optimization and optimal control, renewable energy and sustainability, artificial intelligence and operational research, economics and management, smart cities and rural planning, meta-heuristics and big data analytics, cyber security and blockchains, IoTs and Industry 4.0, mathematical modelling and simulation, health care and medicine.

Robust Optimization

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Author : Aharon Ben-Tal
language : en
Publisher: Princeton University Press
Release Date : 2009-08-10

Robust Optimization written by Aharon Ben-Tal and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-10 with Mathematics categories.

Robust optimization is still a relatively new approach to optimization problems affected by uncertainty, but it has already proved so useful in real applications that it is difficult to tackle such problems today without considering this powerful methodology. Written by the principal developers of robust optimization, and describing the main achievements of a decade of research, this is the first book to provide a comprehensive and up-to-date account of the subject. Robust optimization is designed to meet some major challenges associated with uncertainty-affected optimization problems: to operate under lack of full information on the nature of uncertainty; to model the problem in a form that can be solved efficiently; and to provide guarantees about the performance of the solution. The book starts with a relatively simple treatment of uncertain linear programming, proceeding with a deep analysis of the interconnections between the construction of appropriate uncertainty sets and the classical chance constraints (probabilistic) approach. It then develops the robust optimization theory for uncertain conic quadratic and semidefinite optimization problems and dynamic (multistage) problems. The theory is supported by numerous examples and computational illustrations. An essential book for anyone working on optimization and decision making under uncertainty, Robust Optimization also makes an ideal graduate textbook on the subject.

Operator Analysis

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Author : Jim Agler
language : en
Publisher: Cambridge University Press
Release Date : 2020-03-26

Operator Analysis written by Jim Agler and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-26 with Mathematics categories.

This monograph, aimed at graduate students and researchers, explores the use of Hilbert space methods in function theory. Explaining how operator theory interacts with function theory in one and several variables, the authors journey from an accessible explanation of the techniques to their uses in cutting edge research.