1 Preliminary Knowledge
1.1 Nomenclatures
1.2 Convex Sets and Convex Functions
1.3 Convex Optimization
1.3.1 Gradient Descent and Coordinate Descent
1.3.2 Karush-Kuhn-Tucker KKT Conditions
1.4 Some Lemmas in Linear Algebra
1.5 A Brief Introduction of CVX Toolbox
Problems
References
2 Support Vector Machines
2.1 Basic SVM
2.2 Soft Margin SVM
2.3 Kernel SVM
2.4 Multi-kernel SVM
2.5 Multi-class SVM
2.6 Decomposition and SMO
2.7 Further Discussions
Problems
References
3 Parameter Estimations
3.1 Maximum Likelihood Estimation
3.2 Measurements with iid Noise
3.3 Expectation Maximization for Mixture Models
3.4 The General Expectation Maximization
3.5 Expectation Maximization for PPCA Model with Missing Data
3.6 K-Means Clustering
Problems
References
4 Norm Approximation and Regularization
4.1 Norm Approximation
4.2 Tikhonov Regularization
4.3 1-Norm Regularization for Sparsity
4.4 Regularization and MAP Estimation
Problems
References
5 Semidefinite Programming and Linear Matrix Inequalities
5.1 Semidefinite Matrix and Semidefinite Programming
5.2 LMI and Classical Linear Control Problems
5.2.1 Stability of Continuous-Time Linear Systems
5.2.2 Stability of Discrete-Time Linear Systems..''
5.2.3 LMI and Algebraic Riccati Equations
5.3 LMI and Linear Systems with Time Delay
Problems
References
6 Convex Relaxation
6.1 Basic Idea of Convex Relaxation
6.2 Max-Cut Problem
6.3 Solving Sudoku Puzzle
Problems
References
7 Geometric Problems
7.1 Distances
7.2 Sizes
7.3 Intersection and Containment
Problems
References
Index
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