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.
Sparse Optimization Theory And Methods
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Author : Yun-Bin Zhao
language : en
Publisher: CRC Press
Release Date : 2021-03-31
Sparse Optimization Theory And Methods written by Yun-Bin Zhao and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-31 with Mathematical optimization categories.
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
Optimization
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Author : Mohan C. Joshi
language : en
Publisher: Alpha Science Int'l Ltd.
Release Date : 2004
Optimization written by Mohan C. Joshi and has been published by Alpha Science Int'l Ltd. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Computers categories.
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.
Polynomial Optimization Moments And Applications
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Author : Michal Kočvara
language : en
Publisher: Springer Nature
Release Date : 2024-01-28
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 2024-01-28 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 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.
Optimization Theory And Practice
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Author : Wilhelm Forst
language : en
Publisher:
Release Date : 2010
Optimization Theory And Practice written by Wilhelm Forst and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Algebra categories.
Optimization
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Author :
language : en
Publisher:
Release Date : 2010
Optimization written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Algebra categories.
Genericity In Polynomial Optimization
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Author : Tien Son Pham
language : en
Publisher: World Scientific
Release Date : 2016-12-22
Genericity In Polynomial Optimization written by Tien Son Pham and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-22 with Mathematics categories.
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.
Optimization
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Author : Jean-Bapiste Hiriart-Urruty
language : en
Publisher: CRC Press
Release Date : 2020-11-26
Optimization written by Jean-Bapiste Hiriart-Urruty and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-26 with Mathematics categories.
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.
Global Optimization
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Author : Marco Locatelli
language : en
Publisher: SIAM
Release Date : 2013-10-16
Global Optimization written by Marco Locatelli and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-16 with Mathematics categories.
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.
Optimization Theory And Practice
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Author : Gordon S. G. Beveridge
language : en
Publisher: McGraw-Hill Companies
Release Date : 1970
Optimization Theory And Practice written by Gordon S. G. Beveridge and has been published by McGraw-Hill Companies this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Mathematics categories.
"In general, this presentation demonstrates the interrelationships between the various facets of optimization. These aspects range from the differential calculus through direct search and mathematical programming techniques to the more specialized game theory and decision theory required when competition is present. The integrated approach is seen, for instance, in the discussion of multidimensional numerical search techniques . Each search may be characterized by the two essential features of a distance and direction of movement. These, together with a further classification based on whether or not the gradient is required, have provided the framework within which search methods are presented. In this context the similarities and differences, the advantages and disadvantages, and the range of applicabilities and failures of all search techniques can be clearly understood. Thus such well-known search methods as Rosen's gradient projection and Zoutendijk's feasible directions are seen to stem from the same basic concept, namely, local linearization. A second example of the interrelationship of methods is the evolution from the Lagrangian formulation of such diverse techniques as the so-called discrete maximum principle, the maximum principle of Pontryagin, duals in linear problems, the Kuhn-Tucker conditions, steepest ascent, the gradient projection, and other important techniques."--Preface.