凸优化

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

Ⅰ 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

……

Ⅱ Applications

Ⅲ Algorithms

Appendices

References

Notation

Index

This book is about conuer optimization， a special class of mathematical optimization problems， which includes least-squares and linear programming problems. It is well known that least-squares and linear programming problems have a fairly complete theory， arise in a variety of applications， and can be solved numerically very efficiently. The basic point of this book is that the same can be said for the larger class of convex optimization problems.