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Optimization for Signal Processing
Welcome
Foundation
1. Set Theory
1.1. Sets
1.2. Relations
1.3. Functions
1.4. Cardinality
1.5. Sequences
1.6. General Cartesian Product
2. Elementary Real Analysis
2.1. Real Line
2.2. Topology of Real Line
2.3. Sequences and Series
2.4. The Extended Real Line
2.5. Real Valued Functions
2.6. Real Functions
2.7. Differentiable Functions
2.8. Some Important Inequalities
3. Metric Spaces
3.1. Introduction
3.2. Metric Topology
3.3. Boundedness
3.4. Sequences
3.5. Subspace Topology
3.6. Functions and Continuity
3.7. Completeness
3.8. Compactness
3.9. Real Valued Functions
3.10. Discrete Metric Space
3.11. Special Topics
4. Linear Algebra
4.1. Matrices
4.2. Vector Spaces
4.3. Linear Transformations
4.4. Normed Linear Spaces
4.5. Inner Product Spaces
4.6. Dual Spaces
4.7. The Euclidean Space
4.8. Symmetric Matrices
4.9. Important Vector Spaces
4.10. Sequence Spaces
4.11. Affine Sets and Transformations
5. Multivariate Calculus
5.1. Differentiation
5.2. Differentiation in Banach Spaces
6. Numerical Optimization
6.1. Mathematical Optimization
Convexity
7. Convex Sets and Functions
7.1. Real Vector Spaces
7.2. Convex Sets
7.3. Convex Subsets of
\(\RR^n\)
7.4. Cones
7.5. Cones II
7.6. Cones III
7.7. Generalized Inequalities
7.8. Convex Functions
7.9. Differentiability and Convex Functions
7.10. Function Operations
7.11. Topology of Convex Sets
7.12. Separation Theorems
7.13. Continuity
7.14. Recession Cones
7.15. Directional Derivatives
7.16. Subgradients
7.17. Conjugate Functions
7.18. Smoothness
7.19. Infimal Convolution
8. Convex Optimization
8.1. Convex Optimization
8.2. Projection on Convex Sets
8.3. Directions of Recession
8.4. Basic Duality
8.5. Constrained Optimization I
8.6. Linear Constraints
8.7. Constrained Optimization II
8.8. Lagrange Multipliers
8.9. Lagrangian Duality
8.10. Conjugate Duality
8.11. Linear Programming
8.12. Quadratic Programming
9. Subgradient Methods
9.1. Basic Subgradient Method
10. Proximal Algorithms
10.3. Proximal Mappings and Operators
Sparsity
11. Sparse Signal Models
11.3. Underdetermined Linear Systems
11.4. Sparsity in Orthonormal Bases
11.5. Sparse and Redundant Representations
11.6. Dictionaries
11.7. Compressive Sensing
Epilogue
Notation
Bibliographic Notes
Index
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Subgradient Methods
9.
Subgradient Methods
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