凸最佳化套用講義

《凸最佳化套用講義》 是2015年清華大學出版社出版的圖書，作者是李力。

基本介紹

• 中文名：凸最佳化套用講義
• 作者：李力
• 出版社： 清華大學出版社
• 出版時間：2015年06月01日
• ISBN：9787302390299

內容簡介

凸最佳化理論和方法能夠解決一大類常見的最佳化問題。本書介紹了凸最佳化在支撐向量機、參數估計、範數逼近、控制器設計等問題中的套用，以期讀者掌握將實際問題轉換（或近似轉換）成凸最佳化問題的基本知識和基本方法，能夠靈活使用凸最佳化理論和方法解決實際問題。

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