Optimal Quadratic Programming Algorithms
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Optimal Quadratic Programming Algorithms
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Author : Zdenek Dostál
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-04-03
Optimal Quadratic Programming Algorithms written by Zdenek Dostál 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 2009-04-03 with Mathematics categories.
Solving optimization problems in complex systems often requires the implementation of advanced mathematical techniques. Quadratic programming (QP) is one technique that allows for the optimization of a quadratic function in several variables in the presence of linear constraints. QP problems arise in fields as diverse as electrical engineering, agricultural planning, and optics. Given its broad applicability, a comprehensive understanding of quadratic programming is a valuable resource in nearly every scientific field. Optimal Quadratic Programming Algorithms presents recently developed algorithms for solving large QP problems. The presentation focuses on algorithms which are, in a sense optimal, i.e., they can solve important classes of problems at a cost proportional to the number of unknowns. For each algorithm presented, the book details its classical predecessor, describes its drawbacks, introduces modifications that improve its performance, and demonstrates these improvements through numerical experiments. This self-contained monograph can serve as an introductory text on quadratic programming for graduate students and researchers. Additionally, since the solution of many nonlinear problems can be reduced to the solution of a sequence of QP problems, it can also be used as a convenient introduction to nonlinear programming. The reader is required to have a basic knowledge of calculus in several variables and linear algebra.
Optimal Quadratic Programming Algorithms
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Author : Zdenek Dostál
language : en
Publisher: Springer
Release Date : 2008-11-01
Optimal Quadratic Programming Algorithms written by Zdenek Dostál and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-01 with Mathematics categories.
Quadratic programming (QP) is one advanced mathematical technique that allows for the optimization of a quadratic function in several variables in the presence of linear constraints. This book presents recently developed algorithms for solving large QP problems and focuses on algorithms which are, in a sense optimal, i.e., they can solve important classes of problems at a cost proportional to the number of unknowns. For each algorithm presented, the book details its classical predecessor, describes its drawbacks, introduces modifications that improve its performance, and demonstrates these improvements through numerical experiments. This self-contained monograph can serve as an introductory text on quadratic programming for graduate students and researchers. Additionally, since the solution of many nonlinear problems can be reduced to the solution of a sequence of QP problems, it can also be used as a convenient introduction to nonlinear programming.
Quadratic Programming With Computer Programs
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Author : Michael J. Best
language : en
Publisher: CRC Press
Release Date : 2017-07-12
Quadratic Programming With Computer Programs written by Michael J. Best and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-12 with Business & Economics categories.
Quadratic programming is a mathematical technique that allows for the optimization of a quadratic function in several variables. QP is a subset of Operations Research and is the next higher lever of sophistication than Linear Programming. It is a key mathematical tool in Portfolio Optimization and structural plasticity. This is useful in Civil Engineering as well as Statistics.
Complexity In Numerical Optimization
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Author : Panos M. Pardalos
language : en
Publisher: World Scientific
Release Date : 1993
Complexity In Numerical Optimization written by Panos M. Pardalos and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
Computational complexity, originated from the interactions between computer science and numerical optimization, is one of the major theories that have revolutionized the approach to solving optimization problems and to analyzing their intrinsic difficulty.The main focus of complexity is the study of whether existing algorithms are efficient for the solution of problems, and which problems are likely to be tractable.The quest for developing efficient algorithms leads also to elegant general approaches for solving optimization problems, and reveals surprising connections among problems and their solutions.This book is a collection of articles on recent complexity developments in numerical optimization. The topics covered include complexity of approximation algorithms, new polynomial time algorithms for convex quadratic minimization, interior point algorithms, complexity issues regarding test generation of NP-hard problems, complexity of scheduling problems, min-max, fractional combinatorial optimization, fixed point computations and network flow problems.The collection of articles provide a broad spectrum of the direction in which research is going and help to elucidate the nature of computational complexity in optimization. The book will be a valuable source of information to faculty, students and researchers in numerical optimization and related areas.
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.
Algorithms For Optimization
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Author : Mykel J. Kochenderfer
language : en
Publisher: MIT Press
Release Date : 2019-03-12
Algorithms For Optimization written by Mykel J. Kochenderfer and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-12 with Computers categories.
A comprehensive introduction to optimization with a focus on practical algorithms for the design of engineering systems. This book offers a comprehensive introduction to optimization with a focus on practical algorithms. The book approaches optimization from an engineering perspective, where the objective is to design a system that optimizes a set of metrics subject to constraints. Readers will learn about computational approaches for a range of challenges, including searching high-dimensional spaces, handling problems where there are multiple competing objectives, and accommodating uncertainty in the metrics. Figures, examples, and exercises convey the intuition behind the mathematical approaches. The text provides concrete implementations in the Julia programming language. Topics covered include derivatives and their generalization to multiple dimensions; local descent and first- and second-order methods that inform local descent; stochastic methods, which introduce randomness into the optimization process; linear constrained optimization, when both the objective function and the constraints are linear; surrogate models, probabilistic surrogate models, and using probabilistic surrogate models to guide optimization; optimization under uncertainty; uncertainty propagation; expression optimization; and multidisciplinary design optimization. Appendixes offer an introduction to the Julia language, test functions for evaluating algorithm performance, and mathematical concepts used in the derivation and analysis of the optimization methods discussed in the text. The book can be used by advanced undergraduates and graduate students in mathematics, statistics, computer science, any engineering field, (including electrical engineering and aerospace engineering), and operations research, and as a reference for professionals.
The Linear Complementarity Problem
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Author : Richard W. Cottle
language : en
Publisher: SIAM
Release Date : 2009-08-27
The Linear Complementarity Problem written by Richard W. Cottle and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-27 with Mathematics categories.
A revised edition of the standard reference on the linear complementarity problem.
Nonlinear Optimization
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Author : Stephen A. Vavasis
language : en
Publisher: Oxford University Press, USA
Release Date : 1991
Nonlinear Optimization written by Stephen A. Vavasis and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Computers categories.
The fields of computer science and optimization greatly influence each other, and this book is about one important connection between the two: complexity theory. Complexity theory underlies computer algorithms and is used to address such questions as the efficiency of algorithms and the possibility of algorithmic solutions for particular problems. Furthermore, as optimization problems increase in size with hardware capacity, complexity theory plays a steadily growing role in the exploration of optimization algorithms. As larger and more complicated problems are addressed, it is more important than ever to understand the asymptotic complexity issues. This book describes some of the key developments in the complexity aspects of optimization during the last decade. It will be a valuable source of information for computer scientists and computational mathematicians.
A Java Library Of Graph Algorithms And Optimization
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Author : Hang T. Lau
language : en
Publisher: CRC Press
Release Date : 2006-10-20
A Java Library Of Graph Algorithms And Optimization written by Hang T. Lau and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-10-20 with Computers categories.
Because of its portability and platform-independence, Java is the ideal computer programming language to use when working on graph algorithms and other mathematical programming problems. Collecting some of the most popular graph algorithms and optimization procedures, A Java Library of Graph Algorithms and Optimization provides the source code for
Large Scale Sequential Quadratic Programming Algorithms
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Author : Stanford University. Department of Operations Research. Systems Optimization Laboratory
language : en
Publisher:
Release Date : 1992
Large Scale Sequential Quadratic Programming Algorithms written by Stanford University. Department of Operations Research. Systems Optimization Laboratory and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with categories.