实例介绍
【实例简介】
optimization models by calafiore
Optimization models Emphasizing practical understanding over the technicalities of specific algorithms, this elegant textbook is an accessible introduction to the field of optimization, focusing on powerful and reliable convex optimization techniques. Students and practitioners will learn how to recognize, simplify, model and solve optimization problems-and apply these basic principles to their own projects a clear and self-contained introduction to linear algebra, accompanied by relevant real-world examples, demonstrates core mathematical concepts in a way that is easy to follow, and helps students to understand their practical relevance Requiring only a basic unders tanding of geometry, calculus, probability and statistics, and striking a careful balance between accessibility and mathematical rigor, it enables students to quickly understand the material, without being overw helmed by complex mathematics Accompanied by numerous end-of-chapter problems, an online solutions manual for instructors, and examples from a diverse range of fields including engineering, data science, economics, finance and management, this is the perfect introduction to optimization for both undergraduate and graduate students GIUSEPPE C. CALAFIORE is an Associate Professor at Dipartimento di automatica e Informatica, Politecnico di torino, and a research fellow of the Institute of electronics, Computer and Telecommunication Engineering, National Research Council of ital LAURENT EL GHAOUI is a Professor in the department of Electrical engineering and computer Science and the Department of Industrial Engineering and Operations research, at the University of California. Berkele Optimization models Giuseppe C calafiore Politecnico di torino Laurent el ghaoui University of california, Berkeley CAMBRIDGE UNIVERSITY PRESS CAMBRIDGE UNIVERSITY PRESS University Printing House, Cambridge CB2 &BS, United K ingdom Cambridge University Press is part of the University of Cambridge It furthers the University's mission by disseminating knowledge in the pursuit of education, learning and research at the highest international levels of excellence www.cambridge.org Informationonthistitlewww.cambridge.org/9781107050877 C Cambridge University Press 2014 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press First published 2014 Printed in the United States of America by Sheridan books, Inc A catalogue record for this publication is available from the British libr IsBN 978-1-107-05087-7 Hardback Internal design based on tufte-latex. googlecode. com Licensed under the apache license, Version 2.0 (the "License); you may not use this file except in compliance with the license. You may obtain a copy of the license at http://www.apache.org/licenses/license-2.0 Unless required by applicable law or agreed to in writing, software distributed under the license is distributed on an"as is " basis, without warranties or conditions of any kind, either express or implied. See the License for the spec ific language governing permissions and limitations under the license Additionalresourcesforthispublicationatwww.cambridge.org/optimizationmodels Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate Dedicated to my parents, and to Charlotte Dedicated to louis, alexandre and camille L ElG Contents Preface 1 ntroduction 1.1 Motivating examples 1. 2 Optimization problems 1.3 Important classes of optimization problems 1. 4 History I Linear algebra models 2 Vectors and functions 2.1 Vector basics 2. 2 Norms and inner products 2.3 Projections onto subspaces 2. 4 Functions 2.5 Exercises 3 Matrices 3. Matrix basics 3.2 Matrices as linear maps 3. 3 Determinants, eigenvalues, and eigenvectors 3.4 Matrices with special structure and properties 3.5 Matrix factorizations 3.6 Matrix norms 3.7 Matrix functions 3.8 Exercises 4 Symmetric matrices 4. Basics 4.2 The spectral theorem 4.3 Spectral decomposition and optimization 4.4 Positive semidefinite matrices 4.5 Exercises 5 Singular value decomposition 5.1 Singular value decomposition 5.2 Matrix properties via SVD 5.3 SVD and optimization 5. 4 Exercises 6 Linear equations and least squares 6.1 Motivation and examples 6.2 The set of solutions of linear equations 6.3 Least-Squares and minimum-norm solutions 6.4 Solving systems of linear equations and ls problems 6.5 Sensitivity of solutions 6.6 Direct and inverse mapping of a unit ball 6.7 Variants of the least-squares problem 6.8 Exercises 7 Matrix algorithms 7. Computing eigenvalues and eigenvectors 7.2 Solving square systems of linear equations 7.3 QR factorization 7.4 Exercises I Convex optimization models 8 Convexity 8. Convex sets 8. 2 Convex functions 8.3 Convex problems 8. 4 Optimality conditions 8.5 Duality 8. 6 Exercises 9 Linear, quadratic, and geometric models 9.1 Unconstrained minimization of quadratic functions 9.2 Geometry of linear and convex quadratic inequalities 9.3 Linear programs 9. 4 Quadratic programs 9.5 Modeling with LP and QP 9.6 LS-related quadratic programs 9.7 Geometric programs 9.8 Exercises 10 Second-order cone and robust models 10.1 Second-order cone programs 10.2 SOCP-representable problems and examples 10.3 Robust optimization models 10.4 Exercises 11 Semidefinite models 11. From linear to conic models 71.2 Linear matrix inequalities 11. 3 Semidefinite programs 11. 4 Examples of SdP models 11.5 Exercises 12 Introduction to algorithms 12. 7 Technical preliminaries 12.2 Algorithms for smooth unconstrained minimization 12.3 Algorithms for smooth convex constrained minimization 12.4 Algorithms for non-smooth convex optimization 12. 5 Coordinate descent methods 12.6 Decentralized optimization methods 12.7 Exercises ⅠIAp plications 13 Learning from data 13.1 Overview of supervised learning 13.2 Least-squares prediction via a pol ynomial model 13.3 Binary classification 13.4 A generic supervised learning problem 13.5 Unsupervised learning 13.6 Exercises 【实例截图】
【核心代码】
optimization models by calafiore
Optimization models Emphasizing practical understanding over the technicalities of specific algorithms, this elegant textbook is an accessible introduction to the field of optimization, focusing on powerful and reliable convex optimization techniques. Students and practitioners will learn how to recognize, simplify, model and solve optimization problems-and apply these basic principles to their own projects a clear and self-contained introduction to linear algebra, accompanied by relevant real-world examples, demonstrates core mathematical concepts in a way that is easy to follow, and helps students to understand their practical relevance Requiring only a basic unders tanding of geometry, calculus, probability and statistics, and striking a careful balance between accessibility and mathematical rigor, it enables students to quickly understand the material, without being overw helmed by complex mathematics Accompanied by numerous end-of-chapter problems, an online solutions manual for instructors, and examples from a diverse range of fields including engineering, data science, economics, finance and management, this is the perfect introduction to optimization for both undergraduate and graduate students GIUSEPPE C. CALAFIORE is an Associate Professor at Dipartimento di automatica e Informatica, Politecnico di torino, and a research fellow of the Institute of electronics, Computer and Telecommunication Engineering, National Research Council of ital LAURENT EL GHAOUI is a Professor in the department of Electrical engineering and computer Science and the Department of Industrial Engineering and Operations research, at the University of California. Berkele Optimization models Giuseppe C calafiore Politecnico di torino Laurent el ghaoui University of california, Berkeley CAMBRIDGE UNIVERSITY PRESS CAMBRIDGE UNIVERSITY PRESS University Printing House, Cambridge CB2 &BS, United K ingdom Cambridge University Press is part of the University of Cambridge It furthers the University's mission by disseminating knowledge in the pursuit of education, learning and research at the highest international levels of excellence www.cambridge.org Informationonthistitlewww.cambridge.org/9781107050877 C Cambridge University Press 2014 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press First published 2014 Printed in the United States of America by Sheridan books, Inc A catalogue record for this publication is available from the British libr IsBN 978-1-107-05087-7 Hardback Internal design based on tufte-latex. googlecode. com Licensed under the apache license, Version 2.0 (the "License); you may not use this file except in compliance with the license. You may obtain a copy of the license at http://www.apache.org/licenses/license-2.0 Unless required by applicable law or agreed to in writing, software distributed under the license is distributed on an"as is " basis, without warranties or conditions of any kind, either express or implied. See the License for the spec ific language governing permissions and limitations under the license Additionalresourcesforthispublicationatwww.cambridge.org/optimizationmodels Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate Dedicated to my parents, and to Charlotte Dedicated to louis, alexandre and camille L ElG Contents Preface 1 ntroduction 1.1 Motivating examples 1. 2 Optimization problems 1.3 Important classes of optimization problems 1. 4 History I Linear algebra models 2 Vectors and functions 2.1 Vector basics 2. 2 Norms and inner products 2.3 Projections onto subspaces 2. 4 Functions 2.5 Exercises 3 Matrices 3. Matrix basics 3.2 Matrices as linear maps 3. 3 Determinants, eigenvalues, and eigenvectors 3.4 Matrices with special structure and properties 3.5 Matrix factorizations 3.6 Matrix norms 3.7 Matrix functions 3.8 Exercises 4 Symmetric matrices 4. Basics 4.2 The spectral theorem 4.3 Spectral decomposition and optimization 4.4 Positive semidefinite matrices 4.5 Exercises 5 Singular value decomposition 5.1 Singular value decomposition 5.2 Matrix properties via SVD 5.3 SVD and optimization 5. 4 Exercises 6 Linear equations and least squares 6.1 Motivation and examples 6.2 The set of solutions of linear equations 6.3 Least-Squares and minimum-norm solutions 6.4 Solving systems of linear equations and ls problems 6.5 Sensitivity of solutions 6.6 Direct and inverse mapping of a unit ball 6.7 Variants of the least-squares problem 6.8 Exercises 7 Matrix algorithms 7. Computing eigenvalues and eigenvectors 7.2 Solving square systems of linear equations 7.3 QR factorization 7.4 Exercises I Convex optimization models 8 Convexity 8. Convex sets 8. 2 Convex functions 8.3 Convex problems 8. 4 Optimality conditions 8.5 Duality 8. 6 Exercises 9 Linear, quadratic, and geometric models 9.1 Unconstrained minimization of quadratic functions 9.2 Geometry of linear and convex quadratic inequalities 9.3 Linear programs 9. 4 Quadratic programs 9.5 Modeling with LP and QP 9.6 LS-related quadratic programs 9.7 Geometric programs 9.8 Exercises 10 Second-order cone and robust models 10.1 Second-order cone programs 10.2 SOCP-representable problems and examples 10.3 Robust optimization models 10.4 Exercises 11 Semidefinite models 11. From linear to conic models 71.2 Linear matrix inequalities 11. 3 Semidefinite programs 11. 4 Examples of SdP models 11.5 Exercises 12 Introduction to algorithms 12. 7 Technical preliminaries 12.2 Algorithms for smooth unconstrained minimization 12.3 Algorithms for smooth convex constrained minimization 12.4 Algorithms for non-smooth convex optimization 12. 5 Coordinate descent methods 12.6 Decentralized optimization methods 12.7 Exercises ⅠIAp plications 13 Learning from data 13.1 Overview of supervised learning 13.2 Least-squares prediction via a pol ynomial model 13.3 Binary classification 13.4 A generic supervised learning problem 13.5 Unsupervised learning 13.6 Exercises 【实例截图】
【核心代码】
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