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1 Automatic code generation for real-time convex optimization&Jacob Mattingley and Stephen Boyd 1

1.1 Introduction 1

1.2 Solvers and specification languages 6

1.3 Examples 12

1.4 Algorithm considerations 22

1.5 Code generation 26

1.6 CVXMOD:a preliminary implementation 28

1.7 Numerical examples 29

1.8 Summary,conclusions,and implications 33

Acknowledgments 35

References 35

2 Gradient-based algorithms with applications to signal-recovery problems&Amir Beck and Marc Teboulle 42

2.1 Introduction 42

2.2 The general optimization model 43

2.3 Building gradient-based schemes 46

2.4 Convergence results for the proximal-gradient method 53

2.5 A fast proximal-gradient method 62

2.6 Algorithms for l1-based regularization problems 67

2.7 TV-based restoration problems 71

2.8 The source-localization problem 77

2.9 Bibliographic notes 83

References 85

3 Graphical models of autoregressive processes&Jitkomut Songsiri,Joachim Dahl,and Lieven Vandenberghe 89

3.1 Introduction 89

3.2 Autoregressive processes 92

3.3 Autoregressive graphical models 98

3.4 Numerical examples 104

3.5 Conclusion 113

Acknowledgments 114

References 114

4 SDP relaxation of homogeneous quadratic optimization:approximation bounds and applications&Zhi-Quan Luo and Tsung-Hui Chang 117

4.1 Introduction 117

4.2 Nonconvex QCQPs and SDP relaxation 118

4.3 SDP relaxation for separable homogeneous QCQPs 123

4.4 SDP relaxation for maximization homogeneous QCQPs 137

4.5 SDP relaxation for fractional QCQPs 143

4.6 More applications of SDP relaxation 156

4.7 Summary and discussion 161

Acknowledgments 162

References 162

5 Probabilistic analysis of semidefinite relaxation detectors for multiple-input,multiple-output systems&Anthony Man-Cho So and Yinyu Ye 166

5.1 Introduction 166

5.2 Problem formulation 169

5.3 Analysis of the SDR detector for the MPSK constellations 172

5.4 Extension to the QAM constellations 179

5.5 Concluding remarks 182

Acknowledgments 182

References 189

6 Semidefinite programming,matrix decomposition,and radar code design&Yongwei Huang,Antonio De Maio,and Shuzhong Zhang 192

6.1 Introduction and notation 192

6.2 Matrix rank-1 decomposition 194

6.3 Semidefinite programming 200

6.4 Quadratically constrained quadratic programming and its SDP relaxation 201

6.5 Polynomially solvable QCQP problems 203

6.6 The radar code-design problem 208

6.7 Performance measures for code design 211

6.8 Optimal code design 214

6.9 Performance analysis 218

6.10 Conclusions 223

References 226

7 Convex analysis for non-negative blind source separation with application in imaging&Wing-Kin Ma,Tsung-Han Chart,Chong-Yung Chi,and Yue Wang 229

7.1 Introduction 229

7.2 Problem statement 231

7.3 Review of some concepts in convex analysis 236

7.4 Non-negative,blind source-separation criterion via CAMNS 238

7.5 Systematic linear-programming method for CAMNS 245

7.6 Alternating volume-maximization heuristics for CAMNS 248

7.7 Numerical results 252

7.8 Summary and discussion 257

Acknowledgments 263

References 263

8 Optimization techniques in modern sampling theory&Tomer Michaeli and Yonina C.Eldar 266

8.1 Introduction 266

8.2 Notation and mathematical preliminaries 268

8.3 Sampling and reconstruction setup 270

8.4 Optimization methods 278

8.5 Subspace priors 280

8.6 Smoothness priors 290

8.7 Comparison of the various scenarios 300

8.8 Sampling with noise 302

8.9 Conclusions 310

Acknowledgments 311

References 311

9 Robust broadband adaptive beamforming using convex optimization&Michael Rübsamen,Amr EI-Keyi,Alex B.Gershman,and Thia Kirubarajan 315

9.1 Introduction 315

9.2 Background 317

9.3 Robust broadband beamformers 321

9.4 Simulations 330

9.5 Conclusions 337

Acknowledgments 337

References 337

10 Cooperative distributed multi-agent optimization&Angelia Nedi？ and Asuman Ozdaglar 340

10.1 Introduction and motivation 340

10.2 Distributed-optimization methods using dual decomposition 343

10.3 Distributed-optimization methods using consensus algorithms 358

10.4 Extensions 372

10.5 Future work 378

10.6 Conclusions 380

10.7 Problems 381

References 384

11 Competitive optimization of cognitive radio MIMO systems via game theory&Gesualso Scutari,Daniel P.Palornar,and Sergio Barbarossa 387

11.1 Introduction and motivation 387

11.2 Strategic non-cooperative games:basic solution concepts and algorithms 393

11.3 Opportunistic communications over unlicensed bands 400

11.4 Opportunistic communications under individual-interference constraints 415

11.5 Opportunistic communications under global-interference constraints 431

11.6 Conclusions 438

Acknowledgments 439

References 439

12 Nash equilibria:the variational approach&Francisco Facchinei and Jong-Shi Pang 443

12.1 Introduction 443

12.2 The Nash-equilibrium problem 444

12.3 Existence theory 455

12.4 Uniqueness theory 466

12.5 Sensitivity analysis 472

12.6 Iterative algorithms 478

12.7 Acommunication game 483

Acknowledgments 490

References 491

Afterword 494

Index 495