Moment Sos Hierarchy The Lectures In Probability Statistics Computational Geometry Control And Nonlinear Pdes

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Moment Sos Hierarchy The Lectures In Probability Statistics Computational Geometry Control And Nonlinear Pdes

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Author : Didier Henrion
language : en
Publisher: World Scientific
Release Date : 2020-11-04

Moment Sos Hierarchy The Lectures In Probability Statistics Computational Geometry Control And Nonlinear Pdes written by Didier Henrion and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-04 with Mathematics categories.

The Moment-SOS hierarchy is a powerful methodology that is used to solve the Generalized Moment Problem (GMP) where the list of applications in various areas of Science and Engineering is almost endless. Initially designed for solving polynomial optimization problems (the simplest example of the GMP), it applies to solving any instance of the GMP whose description only involves semi-algebraic functions and sets. It consists of solving a sequence (a hierarchy) of convex relaxations of the initial problem, and each convex relaxation is a semidefinite program whose size increases in the hierarchy.The goal of this book is to describe in a unified and detailed manner how this methodology applies to solving various problems in different areas ranging from Optimization, Probability, Statistics, Signal Processing, Computational Geometry, Control, Optimal Control and Analysis of a certain class of nonlinear PDEs. For each application, this unconventional methodology differs from traditional approaches and provides an unusual viewpoint. Each chapter is devoted to a particular application, where the methodology is thoroughly described and illustrated on some appropriate examples.The exposition is kept at an appropriate level of detail to aid the different levels of readers not necessarily familiar with these tools, to better know and understand this methodology.

The Moment Sos Hierarchy

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Author : Didier Henrion
language : en
Publisher:
Release Date : 2020

The Moment Sos Hierarchy written by Didier Henrion and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Electronic books categories.

The Moment-SOS hierarchy is a powerful methodology that is used to solve the Generalized Moment Problem (GMP) where the list of applications in various areas of Science and Engineering is almost endless. Initially designed for solving polynomial optimization problems (the simplest example of the GMP), it applies to solving any instance of the GMP whose description only involves semi-algebraic functions and sets. It consists of solving a sequence (a hierarchy) of convex relaxations of the initial problem, and each convex relaxation is a semidefinite program whose size increases in the hierarchy.The goal of this book is to describe in a unified and detailed manner how this methodology applies to solving various problems in different areas ranging from Optimization, Probability, Statistics, Signal Processing, Computational Geometry, Control, Optimal Control and Analysis of a certain class of nonlinear PDEs. For each application, this unconventional methodology differs from traditional approaches and provides an unusual viewpoint. Each chapter is devoted to a particular application, where the methodology is thoroughly described and illustrated on some appropriate examples.The exposition is kept at an appropriate level of detail to aid the different levels of readers not necessarily familiar with these tools, to better know and understand this methodology.

Polynomial Optimization Moments And Applications

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Author : Michal Kočvara
language : en
Publisher: Springer Nature
Release Date : 2023-12-27

Polynomial Optimization Moments And Applications written by Michal Kočvara and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-27 with Mathematics categories.

Polynomial optimization is a fascinating field of study that has revolutionized the way we approach nonlinear problems described by polynomial constraints. The applications of this field range from production planning processes to transportation, energy consumption, and resource control. This introductory book explores the latest research developments in polynomial optimization, presenting the results of cutting-edge interdisciplinary work conducted by the European network POEMA. For the past four years, experts from various fields, including algebraists, geometers, computer scientists, and industrial actors, have collaborated in this network to create new methods that go beyond traditional paradigms of mathematical optimization. By exploiting new advances in algebra and convex geometry, these innovative approaches have resulted in significant scientific and technological advancements. This book aims to make these exciting developments accessible to a wider audienceby gathering high-quality chapters on these hot topics. Aimed at both aspiring and established researchers, as well as industry professionals, this book will be an invaluable resource for anyone interested in polynomial optimization and its potential for real-world applications.

Decision And Game Theory For Security

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Author : Branislav Bošanský
language : en
Publisher: Springer Nature
Release Date : 2021-10-30

Decision And Game Theory For Security written by Branislav Bošanský and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-30 with Computers categories.

This book constitutes the refereed proceedings of the 12th International Conference on Decision and Game Theory for Security, GameSec 2021,held in October 2021. Due to COVID-19 pandemic the conference was held virtually. The 20 full papers presented were carefully reviewed and selected from 37 submissions. The papers focus on Theoretical Foundations in Equilibrium Computation; Machine Learning and Game Theory; Ransomware; Cyber-Physical Systems Security; Innovations in Attacks and Defenses.

Counterexamples In Markov Decision Processes

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Author : Alexey B Piunovskiy
language : en
Publisher: World Scientific
Release Date : 2025-03-17

Counterexamples In Markov Decision Processes written by Alexey B Piunovskiy and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-17 with Mathematics categories.

Markov Decision Processes (MDPs) form a cornerstone of applied probability, with over 50 years of rich research history. Throughout this time, numerous foundational books and thousands of journal articles have shaped the field. The central objective of MDP theory is to identify the optimal control strategy for Markov random processes with discrete time. Interestingly, the best control strategies often display unexpected or counterintuitive behaviors, as documented by a wide array of studies.This book gathers some of the most compelling examples of such phenomena while introducing new ones. By doing so, it serves as a valuable companion to existing textbooks. While many examples require little to no prior knowledge, others delve into advanced topics and will primarily interest specialists.In this second edition, extensive revisions have been made, correcting errors and refining the content, with a wealth of new examples added. The range of examples spans from elementary to advanced, requiring background knowledge in areas like measure theory, convex analysis, and advanced probability. A new chapter on continuous time jump processes has also been introduced. The entire text has been reworked for clarity and accessibility.This book is an essential resource for active researchers and graduate students in the field of Markov Decision Processes.

Sparse Polynomial Optimization Theory And Practice

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Author : Victor Magron
language : en
Publisher: World Scientific
Release Date : 2023-04-25

Sparse Polynomial Optimization Theory And Practice written by Victor Magron and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-25 with Mathematics categories.

Many applications, including computer vision, computer arithmetic, deep learning, entanglement in quantum information, graph theory and energy networks, can be successfully tackled within the framework of polynomial optimization, an emerging field with growing research efforts in the last two decades. One key advantage of these techniques is their ability to model a wide range of problems using optimization formulations. Polynomial optimization heavily relies on the moment-sums of squares (moment-SOS) approach proposed by Lasserre, which provides certificates for positive polynomials. On the practical side, however, there is 'no free lunch' and such optimization methods usually encompass severe scalability issues. Fortunately, for many applications, including the ones formerly mentioned, we can look at the problem in the eyes and exploit the inherent data structure arising from the cost and constraints describing the problem.This book presents several research efforts to resolve this scientific challenge with important computational implications. It provides the development of alternative optimization schemes that scale well in terms of computational complexity, at least in some identified class of problems. It also features a unified modeling framework to handle a wide range of applications involving both commutative and noncommutative variables, and to solve concretely large-scale instances. Readers will find a practical section dedicated to the use of available open-source software libraries.This interdisciplinary monograph is essential reading for students, researchers and professionals interested in solving optimization problems with polynomial input data.

Moments Positive Polynomials And Their Applications

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Author : Jean-Bernard Lasserre
language : en
Publisher: World Scientific
Release Date : 2010

Moments Positive Polynomials And Their Applications written by Jean-Bernard Lasserre and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.

Many important problems in global optimization, algebra, probability and statistics, applied mathematics, control theory, financial mathematics, inverse problems, etc. can be modeled as a particular instance of the Generalized Moment Problem (GMP). This book introduces, in a unified manual, a new general methodology to solve the GMP when its data are polynomials and basic semi-algebraic sets. This methodology combines semidefinite programming with recent results from real algebraic geometry to provide a hierarchy of semidefinite relaxations converging to the desired optimal value. Applied on appropriate cones, standard duality in convex optimization nicely expresses the duality between moments and positive polynomials. In the second part of this invaluable volume, the methodology is particularized and described in detail for various applications, including global optimization, probability, optimal context, mathematical finance, multivariate integration, etc., and examples are provided for each particular application.

Mathematics And Computation

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Author : Avi Wigderson
language : en
Publisher: Princeton University Press
Release Date : 2019-10-29

Mathematics And Computation written by Avi Wigderson 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 2019-10-29 with Computers categories.

From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography

Foundations Of Computational Mathematics

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Author : Ronald A. DeVore
language : en
Publisher: Cambridge University Press
Release Date : 2001-05-17

Foundations Of Computational Mathematics written by Ronald A. DeVore 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 2001-05-17 with Mathematics categories.

Collection of papers by leading researchers in computational mathematics, suitable for graduate students and researchers.

Proceedings Of The International Congress Of Mathematicians 2018 Icm 2018 In 4 Volumes

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Author : Boyan Sirakov
language : en
Publisher: World Scientific
Release Date : 2019-02-27

Proceedings Of The International Congress Of Mathematicians 2018 Icm 2018 In 4 Volumes written by Boyan Sirakov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-27 with Mathematics categories.

The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.