Sparse Polynomial Optimization Theory And Practice

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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.

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.

Formal Methods

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Author : André Platzer
language : en
Publisher: Springer Nature
Release Date : 2024-09-10

Formal Methods written by André Platzer and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-10 with Computers categories.

The open access book set LNCS 14933 + 14934 constitutes the refereed proceedings of the 26th International Symposium on Formal Methods, FM 2024, which took place in Milan, Italy, in September 2024. The 51 full and 4 short papers included in these proceedings were carefully reviewed and selected from 219 submissions. They also include 2 invited talks in full paper length and 10 tutorial papers. The contributions were organized in topical sections as follows: Part I: Invited papers; fundamentals of formal verification; foundations; learn and repair; programming languages.- logic and automata; Part II: Tools and case studies; embedded systems track; industry day track; tutorial papers.

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.

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.

A First Course In Linear Optimization

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Author : Amir Beck
language : en
Publisher: SIAM
Release Date : 2025-05-05

A First Course In Linear Optimization written by Amir Beck and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-05 with Mathematics categories.

This self-contained textbook provides the foundations of linear optimization, covering topics in both continuous and discrete linear optimization. It gradually builds the connection between theory, algorithms, and applications so that readers gain a theoretical and algorithmic foundation, familiarity with a variety of applications, and the ability to apply the theory and algorithms to actual problems. To deepen the reader’s understanding, the authors provide many applications from diverse areas of applied sciences, such as resource allocation, line fitting, graph coloring, the traveling salesman problem, game theory, and network flows; more than 180 exercises, most of them with partial answers and about 70 with complete solutions; and a continuous illustration of the theory through examples and exercises. A First Course in Linear Optimization is intended to be read cover to cover and requires only a first course in linear algebra as a prerequisite. Its 13 chapters can be used as lecture notes for a first course in linear optimization. This book is for a first undergraduate course in linear optimization, such as linear programming, linear optimization, and operations research. It is appropriate for students in operations research, mathematics, economics, and industrial engineering, as well as those studying computer science and engineering disciplines.

Convex Optimization

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Author : Stephen P. Boyd
language : en
Publisher: Cambridge University Press
Release Date : 2004-03-08

Convex Optimization written by Stephen P. Boyd 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 2004-03-08 with Business & Economics categories.

Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.

Mathematical Theory Of Finite Elements

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Author : Leszek F. Demkowicz
language : en
Publisher: SIAM
Release Date : 2023-09-22

Mathematical Theory Of Finite Elements written by Leszek F. Demkowicz and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-22 with Mathematics categories.

This book discusses the foundations of the mathematical theory of finite element methods. The focus is on two subjects: the concept of discrete stability, and the theory of conforming elements forming the exact sequence. Both coercive and noncoercive problems are discussed.. Following the historical path of development, the author covers the Ritz and Galerkin methods to Mikhlin’s theory, followed by the Lax–Milgram theorem and Cea’s lemma to the Babuska theorem and Brezzi’s theory. He finishes with an introduction to the discontinuous Petrov–Galerkin (DPG) method with optimal test functions. Based on the author’s personal lecture notes for a popular version of his graduate course on mathematical theory of finite elements, the book includes a unique exposition of the concept of discrete stability and the means to guarantee it, a coherent presentation of finite elements forming the exact grad-curl-div sequence, and an introduction to the DPG method. Intended for graduate students in computational science, engineering, and mathematics programs, Mathematical Theory of Finite Elements is also appropriate for graduate mathematics and mathematically oriented engineering students. Instructors will find the book useful for courses in real analysis, functional analysis, energy (Sobolev) spaces, and Hilbert space methods for PDEs.

Computer Vision Eccv 2024

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Author : Aleš Leonardis
language : en
Publisher: Springer Nature
Release Date : 2024-11-20

Computer Vision Eccv 2024 written by Aleš Leonardis and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-20 with Computers categories.

The multi-volume set of LNCS books with volume numbers 15059 up to 15147 constitutes the refereed proceedings of the 18th European Conference on Computer Vision, ECCV 2024, held in Milan, Italy, during September 29–October 4, 2024. The 2387 papers presented in these proceedings were carefully reviewed and selected from a total of 8585 submissions. They deal with topics such as computer vision; machine learning; deep neural networks; reinforcement learning; object recognition; image classification; image processing; object detection; semantic segmentation; human pose estimation; 3d reconstruction; stereo vision; computational photography; neural networks; image coding; image reconstruction; motion estimation.

Number Theory And Polynomials

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Author : James Fraser McKee
language : en
Publisher: Cambridge University Press
Release Date : 2008-05-08

Number Theory And Polynomials written by James Fraser McKee 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 2008-05-08 with Mathematics categories.

Contributions by leading experts in the field provide a snapshot of current progress in polynomials and number theory.