Sparse Polynomial Optimization Theory And Practice

Author : Victor Magron
Publisher : World Scientific
ISBN 13 : 1800612966
Total Pages : 223 pages
Book Rating : 4.69/5 ( download)

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Download or read book Sparse Polynomial Optimization: Theory And Practice written by Victor Magron and published by World Scientific. This book was released on 2023-04-25 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Michal Kočvara
Publisher : Springer Nature
ISBN 13 : 3031386590
Total Pages : 274 pages
Book Rating : 4.96/5 ( download)

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Download or read book Polynomial Optimization, Moments, and Applications written by Michal Kočvara and published by Springer Nature. This book was released on 2024-01-28 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 audience by 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.

Author : Mohan C. Joshi
Publisher : Alpha Science Int'l Ltd.
ISBN 13 : 9781842651964
Total Pages : 348 pages
Book Rating : 4.6X/5 ( download)

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Download or read book Optimization written by Mohan C. Joshi and published by Alpha Science Int'l Ltd.. This book was released on 2004 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gives a detailed mathematical exposition to various optimization techniques. This book includes topics such as: Single and multi-dimensional optimization, Linear programming, Nonlinear constrained optimization and Evolutionary algorithms.

Author : Yun-Bin Zhao
Publisher : CRC Press
ISBN 13 : 9780367781101
Total Pages : 284 pages
Book Rating : 4.07/5 ( download)

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Download or read book Sparse Optimization Theory and Methods written by Yun-Bin Zhao and published by CRC Press. This book was released on 2021-03-31 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the state-of-the-art in theory and algorithms for signal recovery under the sparsity assumption. The unique conditions for the sparsest solution of underdetermined linear systems are described, and the results for sparse signal recovery under the range space property (RSP) are introduced. This framework is generalized to 1-bit

Author : Wilhelm Forst
Publisher :
ISBN 13 :
Total Pages : 402 pages
Book Rating : 4.62/5 ( download)

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Download or read book Optimization - Theory and Practice written by Wilhelm Forst and published by . This book was released on 2010 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Tien Son Pham
Publisher : World Scientific
ISBN 13 : 1786342235
Total Pages : 260 pages
Book Rating : 4.32/5 ( download)

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Download or read book Genericity In Polynomial Optimization written by Tien Son Pham and published by World Scientific. This book was released on 2016-12-22 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: In full generality, minimizing a polynomial function over a closed semi-algebraic set requires complex mathematical equations. This book explains recent developments from singularity theory and semi-algebraic geometry for studying polynomial optimization problems. Classes of generic problems are defined in a simple and elegant manner by using only the two basic (and relatively simple) notions of Newton polyhedron and non-degeneracy conditions associated with a given polynomial optimization problem. These conditions are well known in singularity theory, however, they are rarely considered within the optimization community.Explanations focus on critical points and tangencies of polynomial optimization, Hölderian error bounds for polynomial systems, Frank-Wolfe-type theorem for polynomial programs and well-posedness in polynomial optimization. It then goes on to look at optimization for the different types of polynomials. Through this text graduate students, PhD students and researchers of mathematics will be provided with the knowledge necessary to use semi-algebraic geometry in optimization.

Author : Jean-Bapiste Hiriart-Urruty
Publisher : CRC Press
ISBN 13 : 1000146367
Total Pages : 275 pages
Book Rating : 4.63/5 ( download)

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Download or read book Optimization written by Jean-Bapiste Hiriart-Urruty and published by CRC Press. This book was released on 2020-11-26 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is concerned with tangent cones, duality formulas, a generalized concept of conjugation, and the notion of maxi-minimizing sequence for a saddle-point problem, and deals more with algorithms in optimization. It focuses on the multiple exchange algorithm in convex programming.

Author : Sabine Burgdorf
Publisher : Springer
ISBN 13 : 3319333380
Total Pages : 118 pages
Book Rating : 4.80/5 ( download)

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Download or read book Optimization of Polynomials in Non-Commuting Variables written by Sabine Burgdorf and published by Springer. This book was released on 2016-06-07 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents recent results on positivity and optimization of polynomials in non-commuting variables. Researchers in non-commutative algebraic geometry, control theory, system engineering, optimization, quantum physics and information science will find the unified notation and mixture of algebraic geometry and mathematical programming useful. Theoretical results are matched with algorithmic considerations; several examples and information on how to use NCSOStools open source package to obtain the results provided. Results are presented on detecting the eigenvalue and trace positivity of polynomials in non-commuting variables using Newton chip method and Newton cyclic chip method, relaxations for constrained and unconstrained optimization problems, semidefinite programming formulations of the relaxations and finite convergence of the hierarchies of these relaxations, and the practical efficiency of algorithms.

Author :
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.62/5 ( download)

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Download or read book Optimization written by and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Marco Locatelli
Publisher : SIAM
ISBN 13 : 1611972663
Total Pages : 439 pages
Book Rating : 4.65/5 ( download)

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Download or read book Global Optimization written by Marco Locatelli and published by SIAM. This book was released on 2013-10-16 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a thorough overview of the rapidly growing field of global optimization, with chapters on key topics such as complexity, heuristic methods, derivation of lower bounds for minimization problems, and branch-and-bound methods and convergence. The final chapter offers both benchmark test problems and applications of global optimization, such as finding the conformation of a molecule or planning an optimal trajectory for interplanetary space travel. An appendix provides fundamental information on convex and concave functions. Intended for Ph.D. students, researchers, and practitioners looking for advanced solution methods to difficult optimization problems. It can be used as a supplementary text in an advanced graduate-level seminar.