Optimization Models 9781107050877

Table of contents :
Calafiore G.C.,Ghaoui L.El. Optimization models (CUP,2014)(ISBN 9781107050877)(600dpi)(648p) ......Page 3
Copyright ......Page 4
Contents vii ......Page 6
Preface page xi ......Page 10
1.1 Motivating examples l ......Page 17
1.2 Optimization problems 5 ......Page 21
1.3 Important classes of optimization problems 10 ......Page 26
1.4 History 14 ......Page 30
I Linear algebra models 19 ......Page 35
2.1 Vector basics 21 ......Page 37
2.2 Norms and inner products 28 ......Page 44
2.3 Projections onto subspaces 37 ......Page 53
2.4 Functions 43 ......Page 59
2.5 Exercises 53 ......Page 69
3.1 Matrix basics 55 ......Page 71
3.2 Matrices as linear maps 61 ......Page 77
3.3 Determinants, eigenvalues, and eigenvectors 64 ......Page 80
3.4 Matrices with special structure and properties 75 ......Page 91
3.5 Matrix factorizations 82 ......Page 98
3.6 Matrix norms 84 ......Page 100
3.7 Matrix functions 87 ......Page 103
3.8 Exercises 91 ......Page 107
4.1 Basics 97 ......Page 113
4.2 The spectral theorem 103 ......Page 119
4.3 Spectral decomposition and optimization 107 ......Page 123
4.4 Positive semidefinite matrices 110 ......Page 126
4.5 Exercises 118 ......Page 134
5.2 Singular value decomposition 123 ......Page 139
5.2 Matrix properties via SVD 127 ......Page 143
5.3 SVD and optimization 133 ......Page 149
5.4 Exercises 145 ......Page 161
6.1 Motivation and examples 151 ......Page 167
6.2 The set of solutions of linear equations 158 ......Page 174
6.3 Least-squares and minimum-norm solutions 160 ......Page 176
6.4 Solving systems of linear equations and LS problems 169 ......Page 185
6.5 Sensitivity of solutions 173 ......Page 189
6.6 Direct and inverse mapping of a unit ball 177 ......Page 193
6.7 Variants of the least-squares problem 183 ......Page 199
6.8 Exercises 193 ......Page 209
7.1 Computing eigenvalues and eigenvectors 199 ......Page 215
7.2 Solving square systems of linear equations 206 ......Page 222
7.3 QR factorization 211 ......Page 227
7.4 Exercises 215 ......Page 231
II Convex optimization models 221 ......Page 237
8.1 Convex sets 223 ......Page 239
8.2 Convex functions 230 ......Page 246
8.3 Convex problems 249 ......Page 265
8.4 Optimality conditions 268 ......Page 284
8.5 Duality 272 ......Page 288
8.6 Exercises 287 ......Page 303
9 Linear, quadratic, and geometric models 293 ......Page 309
9.1 Unconstrained minimization of quadratic functions 294 ......Page 310
9.2 Geometry of linear and convex quadratic inequalities 296 ......Page 312
9.3 Linear programs 302 ......Page 318
9.4 Quadratic programs 311 ......Page 327
9.5 Modeling with LP and QP 320 ......Page 336
9.6 LS-related quadratic programs 331 ......Page 347
9.7 Geometric programs 335......Page 351
9.8 Exercises 341 ......Page 357
10.1 Second-order cone programs 347......Page 363
10.2 SOCP-representable problems and examples 353 ......Page 369
10.3 Robust optimization models 368 ......Page 384
10.4 Exercises 377 ......Page 393
11.1 From linear to conic models 381 ......Page 397
11.2 Linear matrix inequalities 383 ......Page 399
11.3 Semidefinite programs 393 ......Page 409
11.4 Examples of SDP models 399 ......Page 415
11.5 Exercises 418 ......Page 434
12 Introduction to algorithms 425 ......Page 441
12.1 Technical preliminaries 427 ......Page 443
12.2 Algorithms for smooth unconstrained minimization 432 ......Page 448
12.3 Algorithms for smooth convex constrained minimization 452 ......Page 468
12.4 Algorithms for non-smooth convex optimization 472 ......Page 488
12.5 Coordinate descent methods 484 500......Page
12.6 Decentralized optimization methods 487 ......Page 503
12.7 Exercises 496 ......Page 512
III Applications 503 ......Page 519
13.1 Overview of supervised learning 505 ......Page 521
13.2 Least-squares prediction via a polynomial model 507 ......Page 523
13.3 Binary classification 511 ......Page 527
13.4 A generic supervised learning problem 519 ......Page 535
13.5 Unsupervised learning 524 ......Page 540
13.6 Exercises 533 ......Page 549
14.1 Single-period portfolio optimization 539 ......Page 555
14.2 Robust portfolio optimization 546 ......Page 562
14.3 Multi-period portfolio allocation 549 ......Page 565
14.4 Sparse index tracking 556 ......Page 572
14.5 Exercises 558 ......Page 574
15 Control problems 567 ......Page 583
15.1 Continuous and discrete time models 568 ......Page 584
15.2 Optimization-based control synthesis 571 ......Page 587
15.3 Optimization for analysis and controller design 579 ......Page 595
15.4 Exercises 586 ......Page 602
16.1 Digital filter design 591 ......Page 607
16.2 Antenna array design 600 ......Page 616
16.3 Digital circuit design 606 ......Page 622
16.4 Aircraft design 609 ......Page 625
16.5 Supply chain management 613 ......Page 629
16.6 Exercises 622 ......Page 638
Index 627 ......Page 643
cover......Page 1
back cover 632 ......Page 648