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E-raamat: Selected Applications of Convex Optimization

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Selected Applications of Convex OptimizationSuurem pilt
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This book focuses on the applications of convex optimization and highlights several topics, including support vector machines, parameter estimation, norm approximation and regularization, semi-definite programming problems, convex relaxation, and geometric problems. All derivation processes are presented in detail to aid in comprehension. The book offers concrete guidance, helping readers recognize and formulate convex optimization problems they might encounter in practice.

Arvustused

Selected Applications of Convex Optimization is a brief book, only 140 pages, and includes exercises with each chapter. It would be a good supplemental text for an optimization or machine learning course. (John D. Cook, MAA Reviews, maa.org, December, 2015)

1 Preliminary Knowledge
1(16)
1.1 Nomenclatures
1(1)
1.2 Convex Sets and Convex Functions
2(3)
1.3 Convex Optimization
5(5)
1.3.1 Gradient Descent and Coordinate Descent
5(2)
1.3.2 Karush-Kuhn-Tucker (KKT) Conditions
7(3)
1.4 Some Lemmas in Linear Algebra
10(1)
1.5 A Brief Introduction of CVX Toolbox
11(6)
Problems
13(2)
References
15(2)
2 Support Vector Machines
17(36)
2.1 Basic SVM
17(5)
2.2 Soft Margin SVM
22(6)
2.3 Kernel SVM
28(7)
2.4 Multi-kernel SVM
35(3)
2.5 Multi-class SVM
38(7)
2.6 Decomposition and SMO
45(4)
2.7 Further Discussions
49(4)
Problems
49(2)
References
51(2)
3 Parameter Estimations
53(26)
3.1 Maximum Likelihood Estimation
53(6)
3.2 Measurements with iid Noise
59(2)
3.3 Expectation Maximization for Mixture Models
61(5)
3.4 The General Expectation Maximization
66(2)
3.5 Expectation Maximization for PPCA Model with Missing Data
68(5)
3.6 K-Means Clustering
73(6)
Problems
76(1)
References
77(2)
4 Norm Approximation and Regularization
79(20)
4.1 Norm Approximation
79(2)
4.2 Tikhonov Regularization
81(7)
4.3 I-Norm Regularization for Sparsity
88(5)
4.4 Regularization and MAP Estimation
93(6)
Problems
96(1)
References
97(2)
5 Semidefinite Programming and Linear Matrix Inequalities
99(16)
5.1 Semidefinite Matrix and Semidefinite Programming
99(3)
5.2 LMI and Classical Linear Control Problems
102(9)
5.2.1 Stability of Continuous-Time Linear Systems
102(1)
5.2.2 Stability of Discrete-Time Linear Systems
103(3)
5.2.3 LMI and Algebraic Riccati Equations
106(5)
5.3 LMI and Linear Systems with Time Delay
111(4)
Problems
112(1)
References
113(2)
6 Convex Relaxation
115(12)
6.1 Basic Idea of Convex Relaxation
115(3)
6.2 Max-Cut Problem
118(5)
6.3 Solving Sudoku Puzzle
123(4)
Problems
125(1)
References
126(1)
7 Geometric Problems
127(12)
7.1 Distances
127(1)
7.2 Sizes
128(6)
7.3 Intersection and Containment
134(5)
Problems
137(1)
References
138(1)
Index 139
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