凸优化应用讲义

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