Springer Optimization and Its Applications Volume 103:Selected Applications of Convex Optimization

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