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E-raamat: Convex Optimization for Signal Processing and Communications: From Fundamentals to Applications

(National Tsing Hua University, Hsinchu, Taiwan Republic of China), (National Tsing Hua University, Department of Electrical Engin), (National Tsing Hua University, Department of Electrical Engineering, Hsinchu, Taiwan Republic of China)
  • Formaat: 446 pages
  • Ilmumisaeg: 24-Jan-2017
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781498776462
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Convex Optimization for Signal Processing and Communications: From Fundamentals to ApplicationsSuurem pilt
  • Formaat: 446 pages
  • Ilmumisaeg: 24-Jan-2017
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781498776462
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Convex Optimization for Signal Processing and Communications: From Fundamentals to Applications provides fundamental background knowledge of convex optimization, while striking a balance between mathematical theory and applications in signal processing and communications.

In addition to comprehensive proofs and perspective interpretations for core convex optimization theory, this book also provides many insightful figures, remarks, illustrative examples, and guided journeys from theory to cutting-edge research explorations, for efficient and in-depth learning, especially for engineering students and professionals.

With the powerful convex optimization theory and tools, this book provides you with a new degree of freedom and the capability of solving challenging real-world scientific and engineering problems.
Preface xi
1 Mathematical Background 1(34)
1.1 Mathematical prerequisites
1(21)
1.1.1 Vector norm
5(2)
1.1.2 Matrix norm
7(1)
1.1.3 Inner product
8(1)
1.1.4 Norm ball
9(2)
1.1.5 Interior point
11(1)
1.1.6 Complement, scaled sets, and sum of sets
11(1)
1.1.7 Closure and boundary
12(1)
1.1.8 Supremum and infimum
13(2)
1.1.9 Function
15(1)
1.1.10 Continuity
15(1)
1.1.11 Derivative and gradient
16(3)
1.1.12 Hessian
19(1)
1.1.13 Taylor series
20(2)
1.2 Linear algebra revisited
22(9)
1.2.1 Vector subspace
22(1)
1.2.2 Range space, null space, and orthogonal projection
22(2)
1.2.3 Matrix determinant and inverse
24(1)
1.2.4 Positive definiteness and semidefiniteness
24(1)
1.2.5 Eigenvalue decomposition
25(2)
1.2.6 Square root factorization of PSD matrices
27(1)
1.2.7 Singular value decomposition
28(2)
1.2.8 Least-squares approximation
30(1)
1.3 Summary and discussion
31(4)
2 Convex Sets 35(50)
2.1 Affine and convex sets
35(11)
2.1.1 Lines and line segments
35(1)
2.1.2 Affine sets and affine hulls
35(4)
2.1.3 Relative interior and relative boundary
39(1)
2.1.4 Convex sets and convex hulls
40(4)
2.1.5 Cones and conic hulls
44(2)
2.2 Examples of convex sets
46(9)
2.2.1 Hyperplanes and halfspaces
46(2)
2.2.2 Euclidean balls and ellipsoids
48(2)
2.2.3 Polyhedra
50(1)
2.2.4 Simplexes
51(3)
2.2.5 Norm cones
54(1)
2.2.6 Positive semidefinite cones
55(1)
2.3 Convexity preserving operations
55(8)
2.3.1 Intersection
56(1)
2.3.2 Affine function
57(4)
2.3.3 Perspective function and linear-fractional function
61(2)
2.4 Generalized inequalities
63(3)
2.4.1 Proper cones and generalized inequalities
63(1)
2.4.2 Properties of generalized inequalities
64(1)
2.4.3 Minimum and minimal elements
64(2)
2.5 Dual norms and dual cones
66(12)
2.5.1 Dual norms
66(7)
2.5.2 Dual cones
73(5)
2.6 Separating and supporting hyperplanes
78(6)
2.6.1 Separating hyperplane theorem
78(3)
2.6.2 Supporting hyperplanes
81(3)
2.7 Summary and discussion
84(1)
3 Convex Functions 85(50)
3.1 Basic properties and examples of convex functions
85(23)
3.1.1 Definition and fundamental properties
85(6)
3.1.2 First-order condition
91(4)
3.1.3 Second-order condition
95(1)
3.1.4 Examples
96(5)
3.1.5 Epigraph
101(4)
3.1.6 Jensen's inequality
105(3)
3.2 Convexity preserving operations
108(9)
3.2.1 Nonnegative weighted sum
108(1)
3.2.2 Composition with affine mapping
108(1)
3.2.3 Composition (scalar)
109(1)
3.2.4 Pointwise maximum and supremum
110(3)
3.2.5 Pointwise minimum and infimum
113(2)
3.2.6 Perspective of a function
115(2)
3.3 Quasiconvex functions
117(10)
3.3.1 Definition and examples
117(5)
3.3.2 Modified Jensen's inequality
122(1)
3.3.3 First-order condition
123(2)
3.3.4 Second-order condition
125(2)
3.4 Monotonicity on generalized inequalities
127(2)
3.5 Convexity on generalized inequalities
129(4)
3.6 Summary and discussion
133(2)
4 Convex Optimization Problems 135(52)
4.1 Optimization problems in a standard form
136(3)
4.1.1 Some terminologies
136(1)
4.1.2 Optimal value and solution
136(2)
4.1.3 Equivalent problems and feasibility problem
138(1)
4.2 Convex optimization problems
139(12)
4.2.1 Global optimality
140(1)
4.2.2 An optimality criterion
141(10)
4.3 Equivalent representations and transforms
151(12)
4.3.1 Equivalent problem: Epigraph form
151(1)
4.3.2 Equivalent problem: Equality constraint elimination
152(1)
4.3.3 Equivalent problem: Function transformation
152(4)
4.3.4 Equivalent problem: Change of variables
156(2)
4.3.5 Reformulation of complex-variable problems
158(5)
4.4 Convex problems with generalized inequalities
163(9)
4.4.1 Convex problems with generalized inequalitiy constraints
163(1)
4.4.2 Vector optimization
164(8)
4.5 Quasiconvex optimization
172(4)
4.6 Block successive upper bound minimization
176(6)
4.6.1 Stationary point
176(2)
4.6.2 BSUM
178(4)
4.7 Successive convex approximation
182(2)
4.8 Summary and discussion
184(3)
5 Geometric Programming 187(8)
5.1 Some basics
187(1)
5.2 Geometric program (GP)
188(1)
5.3 GP in a convex form
188(2)
5.4 Condensation method
190(3)
5.4.1 Successive GP approximation
191(2)
5.4.2 Physical-layer secret communications
193(1)
5.5 Summary and discussion
193(2)
6 Linear Programming and Quadratic Programming 195(46)
6.1 Linear program (LP)
195(2)
6.2 Examples using LP
197(3)
6.2.1 Diet problem
197(1)
6.2.2 Chebyshev center
197(1)
6.2.3 40-norm approximation
198(1)
6.2.4 Li-norm approximation
199(1)
6.2.5 Maximization/minimization of matrix determinant
199(1)
6.3 Applications in blind source separation using LP/convex geometry
200(23)
6.3.1 nBSS of dependent sources using LP
200(5)
6.3.2 Hyperspectral unmixing using LP
205(5)
6.3.3 Hyperspectral unmixing by simplex geometry
210(13)
6.4 Quadratic program (QP)
223(2)
6.5 Applications of QP and convex geometry in hyperspectral image analysis
225(7)
6.5.1 GENE-CH algorithm for endmember number estimation
227(2)
6.5.2 GENE-AH algorithm for endmember number estimation
229(3)
6.6 Quadratically constrained QP (QCQP)
232(1)
6.7 Applications of QP and QCQP in beamformer design
233(5)
6.7.1 Receive beamforming: Average sidelobe energy minimization
233(2)
6.7.2 Receive beamforming: Worst-case sidelobe energy minimization
235(2)
6.7.3 Transmit beamforming in cognitive radio using QCQP
237(1)
6.8 Summary and discussion
238(3)
7 Second-order Cone Programming 241(16)
7.1 Second-order cone program (SOCP)
241(1)
7.2 Robust linear program
242(1)
7.3 Chance constrained linear program
243(1)
7.4 Robust least-squares approximation
244(1)
7.5 Robust receive beamforming via SOCP
244(4)
7.5.1 Minimum-variance beamformer
245(1)
7.5.2 Robust beamforming via SOCP
246(2)
7.6 Transmit downlink beamforming via SOCP
248(8)
7.6.1 Power minimization beamforming
250(1)
7.6.2 Max-Min-Fair beamforming
251(1)
7.6.3 Multicell beamforming
252(2)
7.6.4 Femtocell beamforming
254(2)
7.7 Summary and discussion
256(1)
8 Semidefinite Programming 257(68)
8.1 Semidefinite program (SDP)
258(1)
8.2 QCQP and SOCP as SDP via Schur complement
259(1)
8.3 S-Procedure
260(2)
8.4 Applications in combinatorial optimization
262(12)
8.4.1 Boolean quadratic program (BQP)
262(1)
8.4.2 Practical example I: MAXCUT
262(2)
8.4.3 Practical example II: ML MIMO detection
264(1)
8.4.4 BQP approximation by semidefinite relaxation
265(4)
8.4.5 Practical example III: Linear fractional SDR (LFSDR) approach to noncoherent ML detection of higher-order QAM OSTBC
269(5)
8.5 Applications in transmit beamforming
274(46)
8.5.1 Downlink beamforming for broadcasting
274(2)
8.5.2 Transmit beamforming in cognitive radio
276(1)
8.5.3 Transmit beamforming in secrecy communication: Artificial noise (AN) aided approach
276(5)
8.5.4 Worst-case robust transmit beamforming: Single-cell MISO scenario
281(4)
8.5.5 Worst-case robust transmit beamforming: Multicell MISO scenario
285(5)
8.5.6 Outage constrained coordinated beamforming for MISO interference channel: Part I (centralized algorithm)
290(9)
8.5.7 Outage constrained coordinated beamforming for MISO interference channel: Part II (efficient algorithms using BSUM)
299(7)
8.5.8 Outage constrained robust transmit beamforming: Single-cell MISO scenario
306(7)
8.5.9 Outage constrained robust transmit beamforming: Multicell MISO scenario
313(7)
8.6 Summary and discussion
320(5)
9 Duality 325(70)
9.1 Lagrange dual function and conjugate function
326(8)
9.1.1 Lagrange dual function
326(3)
9.1.2 Conjugate function
329(4)
9.1.3 Relationship between Lagrange dual function and conjugate function
333(1)
9.2 Lagrange dual problem
334(9)
9.3 Strong duality
343(10)
9.3.1 Slater's condition
343(7)
9.3.2 S-Lemma
350(3)
9.4 Implications of strong duality
353(2)
9.4.1 Max-min characterization of weak and strong duality
353(1)
9.4.2 Certificate of suboptimality
354(1)
9.4.3 Complementary slackness
354(1)
9.5 Karush-Kuhn-Tucker (KKT) optimality conditions
355(10)
9.6 Lagrange dual optimization
365(5)
9.7 Alternating direction method of multipliers (ADMM)
370(3)
9.8 Duality of problems with generalized inequalities
373(11)
9.8.1 Lagrange dual and KKT conditions
373(3)
9.8.2 Lagrange dual of cone program and KKT conditions
376(2)
9.8.3 Lagrange dual of SDP and KKT conditions
378(6)
9.9 Theorems of alternatives
384(9)
9.9.1 Weak alternatives
385(2)
9.9.2 Strong alternatives
387(4)
9.9.3 Proof of S-procedure
391(2)
9.10 Summary and discussion
393(2)
10 Interior-point Methods 395(26)
10.1 Inequality and equality constrained convex problems
395(2)
10.2 Newton's method and barrier function
397(7)
10.2.1 Newton's method for equality constrained problems
397(3)
10.2.2 Barrier function
400(4)
10.3 Central path
404(2)
10.4 Barrier method
406(3)
10.5 Primal-dual interior-point method
409(10)
10.5.1 Primal-dual search direction
410(1)
10.5.2 Surrogate duality gap
411(1)
10.5.3 Primal-dual interior-point algorithm
411(3)
10.5.4 Primal-dual interior-point method for solving SDP
414(5)
10.6 Summary and discussion
419(2)
A Appendix: Convex Optimization Solvers 421(8)
A.1 SeDuMi
421(1)
A.2 CVX
422(1)
A.3 Finite impulse response (FIR) filter design
423(4)
A.3.1 Problem formulation
424(1)
A.3.2 Problem implementation using SeDuMi
425(1)
A.3.3 Problem implementation using CVX
426(1)
A.4 Conclusion
427(2)
Index 429
Dr. Chong-Yung Chi is a Professor, Department of Electrical Engineering (since 1989) and the Institute of Communications Engineering, National Tsing Hua University, Hsinchu, Taiwan. He got his Ph.D. degree in Electrical Engineering from University of Southern California in 1983.His main research interests include signal processing for wireless communications, convex analysis and optimization for blind source separation, biomedical and hyperspectral image analysis. He has published more than 210 technical papers, including more than 75 journal papers (mostly in IEEE Trans. Signal Processing), 4 book chapters and more than 130 peer-reviewed conference papers, as well as a graduate-level textbook, Blind Equalization and System Identification, Springer-Verlag, 2006. Dr. Chi is a senior member of IEEE. He was an Associate Editor (AE) of IEEE Trans. Signal Processing (5/2001~4/2006), IEEE Trans. Circuits and Systems II (1/2006-12/2007), IEEE Trans. Circuits and Systems I (1/2008-12/2009), AE of IEEE Signal Processing Letters (6/2006~5/2010), and a member of Editorial Board of Elsevier Signal Processing (6/2005~5/2008), and an editor (7/2003~12/2005) as well as a Guest Editor (2006) of EURASIP Journal on Applied Signal Processing. Currently, he is a member of Signal Processing for Communications and Networking Technical Committee (SPCOM-TC) and a member of Sensor Array and Multichannel Technical Committee (SAM-TC), IEEE Signal Processing Society, and an AE of IEEE Trans. Signal Processing.



Wei-Chiang Li received the B.S. degree in electrical engineering from the National Tsing Hua University, Hsinchu, Taiwan, in 2009. He is currently pursuing the Ph.D. degree in communications engineering at the National Tsing Hua University, Hsinchu, Taiwan. His research interests are in optimization methods for wireless communications and signal processing.



Chia-Hsiang Lin received the B.S. degree in electrical engineering from the National Tsing Hua University, Hsinchu, Taiwan, in 2010, where he is currently working toward the Ph.D. degree in communications engineering. He is currently a visiting Doctoral Graduate Research Assistant with Virginia Polytechnic Institute and State University, Arlington, VA, USA. His research interests are convex geometry and optimization, network science, game theory, and blind source separation.
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