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E-raamat: Optimization Models

3.88/5 (13 hinnangut Goodreads-ist)
(University of California, Berkeley), (Politecnico di Torino)
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 31-Oct-2014
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781139986007
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Optimization ModelsSuurem pilt
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 31-Oct-2014
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781139986007
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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 principles to their own projects. A clear and self-contained introduction to linear algebra demonstrates core mathematical concepts in a way that is easy to follow, and helps students to understand their practical relevance. Requiring only a basic understanding of geometry, calculus, probability and statistics, and striking a careful balance between accessibility and rigor, it enables students to quickly understand the material, without being overwhelmed by complex mathematics. Accompanied by numerous end-of-chapter problems, an online solutions manual for instructors, and relevant examples from diverse fields including engineering, data science, economics, finance, and management, this is the perfect introduction to optimization for undergraduate and graduate students.

Emphasizing practical understanding over the technicalities of specific algorithms, this elegant textbook teaches students how to recognize, simplify, model and solve optimization problems – and apply these basic principles to their own projects. Accompanied by an online solution manual, accessible only to instructors.

Arvustused

'In Optimization Models, Calafiore and El Ghaoui have created a beautiful and very much needed on-ramp to the world of modern mathematical optimization and its wide range of applications. They lead an undergraduate, with not much more than basic calculus behind her, from the basics of linear algebra all the way to modern optimization-based machine learning, image processing, control, and finance, to name just a few applications. Until now, these methods and topics were accessible only to graduate students in a few fields, and the few undergraduates who brave the daunting prerequisites. The book's seamless integration of mathematics and applications, and its focus on modeling practical problems and algorithmic solution methods, will be very appealing to a wide audience.' Stephen Boyd, Stanford University, California

Muu info

This accessible textbook demonstrates how to recognize, simplify, model and solve optimization problems and apply these principles to new projects.
Preface xi
1 Introduction
1(18)
1.1 Motivating examples
1(4)
1.2 Optimization problems
5(5)
1.3 Important classes of optimization problems
10(4)
1.4 History
14(5)
I Linear algebra models
19(202)
2 Vectors and functions
21(34)
2.1 Vector basics
21(7)
2.2 Norms and inner products
28(9)
2.3 Projections onto subspaces
37(6)
2.4 Functions
43(10)
2.5 Exercises
53(2)
3 Matrices
55(42)
3.1 Matrix basics
55(6)
3.2 Matrices as linear maps
61(3)
3.3 Determinants, eigenvalues, and eigenvectors
64(11)
3.4 Matrices with special structure and properties
75(7)
3.5 Matrix factorizations
82(2)
3.6 Matrix norms
84(3)
3.7 Matrix functions
87(4)
3.8 Exercises
91(6)
4 Symmetric matrices
97(26)
4.1 Basics
97(6)
4.2 The spectral theorem
103(4)
4.3 Spectral decomposition and optimization
107(3)
4.4 Positive semidefinite matrices
110(8)
4.5 Exercises
118(5)
5 Singular value decomposition
123(28)
5.1 Singular value decomposition
123(4)
5.2 Matrix properties via SVD
127(6)
5.3 SVD and optimization
133(12)
5.4 Exercises
145(6)
6 Linear equations and least squares
151(48)
6.1 Motivation and examples
151(7)
6.2 The set of solutions of linear equations
158(2)
6.3 Least-squares and minimum-norm solutions
160(9)
6.4 Solving systems of linear equations and LS problems
169(4)
6.5 Sensitivity of solutions
173(4)
6.6 Direct and inverse mapping of a unit ball
177(6)
6.7 Variants of the least-squares problem
183(10)
6.8 Exercises
193(6)
7 Matrix algorithms
199(22)
7.1 Computing eigenvalues and eigenvectors
199(7)
7.2 Solving square systems of linear equations
206(5)
7.3 QR factorization
211(4)
7.4 Exercises
215(6)
II Convex optimization models
221(282)
8 Convexity
223(70)
8.1 Convex sets
223(7)
8.2 Convex functions
230(19)
8.3 Convex problems
249(19)
8.4 Optimality conditions
268(4)
8.5 Duality
272(15)
8.6 Exercises
287(6)
9 Linear, quadratic, and geometric models
293(54)
9.1 Unconstrained minimization of quadratic functions
294(2)
9.2 Geometry of linear and convex quadratic inequalities
296(6)
9.3 Linear programs
302(9)
9.4 Quadratic programs
311(9)
9.5 Modeling with LP and QP
320(11)
9.6 LS-related quadratic programs
331(4)
9.7 Geometric programs
335(6)
9.8 Exercises
341(6)
10 Second-order cone and robust models
347(34)
10.1 Second-order cone programs
347(6)
10.2 SOCP-representable problems and examples
353(15)
10.3 Robust optimization models
368(9)
10.4 Exercises
377(4)
11 Semidefinite models
381(44)
11.1 From linear to conic models
381(2)
11.2 Linear matrix inequalities
383(10)
11.3 Semidefinite programs
393(6)
11.4 Examples of SDP models
399(19)
11.5 Exercises
418(7)
12 Introduction to algorithms
425(78)
12.1 Technical preliminaries
427(5)
12.2 Algorithms for smooth unconstrained minimization
432(20)
12.3 Algorithms for smooth convex constrained minimization
452(20)
12.4 Algorithms for non-smooth convex optimization
472(12)
12.5 Coordinate descent methods
484(3)
12.6 Decentralized optimization methods
487(9)
12.7 Exercises
496(7)
III Applications
503(124)
13 Learning from data
505(34)
13.1 Overview of supervised learning
505(2)
13.2 Least-squares prediction via a polynomial model
507(4)
13.3 Binary classification
511(8)
13.4 A generic supervised learning problem
519(5)
13.5 Unsupervised learning
524(9)
13.6 Exercises
533(6)
14 Computational finance
539(28)
14.1 Single-period portfolio optimization
539(7)
14.2 Robust portfolio optimization
546(3)
14.3 Multi-period portfolio allocation
549(7)
14.4 Sparse index tracking
556(2)
14.5 Exercises
558(9)
15 Control problems
567(24)
15.1 Continuous and discrete time models
568(3)
15.2 Optimization-based control synthesis
571(8)
15.3 Optimization for analysis and controller design
579(7)
15.4 Exercises
586(5)
16 Engineering design
591(36)
16.1 Digital filter design
591(9)
16.2 Antenna array design
600(6)
16.3 Digital circuit design
606(3)
16.4 Aircraft design
609(4)
16.5 Supply chain management
613(9)
16.6 Exercises
622(5)
Index 627
Giuseppe C. Calafiore is an Associate Professor at the 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 Italy. Laurent El Ghaoui is a Professor in the Department of Electrical Engineering and Computer Science, the Department of Industrial Engineering and Operations Research, and the Berkeley Center for New Media, at the University of California, Berkeley.
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