Presents applications of convex optimization issues arranged in a synthetic way
Demonstrates the interplay of convex optimization theory and applications of carefully designed Matlab sample codes
Introduces all derivation processes in details so that readers can teach themselves without any difficulties
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.
Content Level » Research
Keywords » Convex Optimization - Convex Relaxation - Expectation Maximization - Linear Matrix Inequalities - Support Vector Machines - data mining
Related subjects » Applications - Computational Science & Engineering - Mathematics
Author(s): Li Li
Series: Springer Optimization and Its Applications 103
Publisher: Springer
Year: 2015
Language: English
Pages: C, X, 140
Tags: Математика;Методы оптимизации;
Cover
Springer Optimization and Its Applications, Volume 103
Selected Applications of Convex Optimization
Copyright
© Tsinghua University Press, Beijing and Springer-Verlag Berlin Heidelberg 2015
ISSN 1931-6828
ISSN 1931-6836 (electronic)
ISBN 978-3-662-46355-0
ISBN 978-3-662-46356-7 (eBook)
DOI 10.1007/978-3-662-46356-7
Dedication
Preface
Contents
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
