Convex optimization for signal processing and communications : from fundamentals to applications /
"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 compre...
| Main Authors: | , , |
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| Corporate Author: | |
| Format: | eBook |
| Language: | English |
| Published: |
Boca Raton :
CRC Press,
[2017]
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| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- Cover ; Half Title ; Title Page ; Copyright Page ; Table of Contents ; Preface ; 1: Mathematical Background ; 1.1 Mathematical prerequisites ; 1.1.1 Vector norm ; 1.1.2 Matrix norm ; 1.1.3 Inner product ; 1.1.4 Norm ball ; 1.1.5 Interior point.
- 1.1.6 Complement, scaled sets, and sum of sets 1.1.7 Closure and boundary ; 1.1.8 Supremum and infimum ; 1.1.9 Function ; 1.1.10 Continuity ; 1.1.11 Derivative and gradient ; 1.1.12 Hessian ; 1.1.13 Taylor series ; 1.2 Linear algebra revisited ; 1.2.1 Vector subspace.
- 1.2.2 Range space, null space, and orthogonal projection 1.2.3 Matrix determinant and inverse ; 1.2.4 Positive definiteness and semidefiniteness ; 1.2.5 Eigenvalue decomposition ; 1.2.6 Square root factorization of PSD matrices ; 1.2.7 Singular value decomposition.
- 1.2.8 Least-squares approximation 1.3 Summary and discussion ; 2: Convex Sets ; 2.1 Affine and convex sets ; 2.1.1 Lines and line segments ; 2.1.2 Affine sets and affine hulls ; 2.1.3 Relative interior and relative boundary ; 2.1.4 Convex sets and convex hulls.
- 2.1.5 Cones and conic hulls 2.2 Examples of convex sets ; 2.2.1 Hyperplanes and halfspaces ; 2.2.2 Euclidean balls and ellipsoids ; 2.2.3 Polyhedra ; 2.2.4 Simplexes ; 2.2.5 Norm cones ; 2.2.6 Positive semidefinite cones ; 2.3 Convexity preserving operations ; 2.3.1 Intersection.