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凸優化理論和方法能夠解決一大類常見的優化問題。本書介紹瞭凸優化在支撐嚮量機、參數估計、範數逼近、控製器設計等問題中的應用,以期讀者掌握將實際問題轉換(或近似轉換)成凸優化問題的基本知識和基本方法,能夠靈活使用凸優化理論和方法解決實際問題。
內容簡介
凸優化理論和方法能夠解決一大類常見的優化問題。李力編著的這本《凸優化應用講義(英文版)》介紹瞭凸優化在支撐嚮量機、參數估計、範數逼近、控製器設計等問題中的應用,以期讀者掌握將實際問題轉換(或近似轉換)成凸優化問題的基本知識和基本方法,能夠靈活使用凸優化理論和方法解決實際問題。
本書潛在的讀者包括運籌優化方嚮、機器學習方嚮、統計方嚮、控製方嚮、信號處理方嚮的研究生和高年級本科生。讀者需對凸優化理論和綫性代數理論有一定的瞭解。
目錄
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
前言/序言
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