凸優化

Preface

Introduction

1.1 Mathematical optimization

1.2 Least-squares and linear programming

1.3 Convex optimization

1.4 Nonlinear optimization

1.5 Outline

1.6 Notation

Bibliography

Theory

Convex sets

2.1 Affine and convex sets

2.2 Some important examples

2.3 Operations that preserve convexity

2.4 Generalized inequalities

2.5 Separating and supporting hyperplanes

2.6 Dual cones and generalized inequalities

Bibliography

Exercises

Convex functions

3.1 Basic properties and examples

3.2 Operations that preserve convexity

3.3 The conjugate function

3.4 Quasiconvex functions

3.5 Log-concave and log-convex functions

3.6 Convexity with respect to generalized inequalities.

Bibliography

Exercises