鲍迪编著的《凸优化》内容非常丰富。理论部分由4章构成,不仅涵盖了凸优化的所有基本概念和主要结果,还详细介绍了几类基本的凸优化问题以及将特殊的优化问题表述为凸优化问题的变换方法,这些内容对灵活运用凸优化知识解决实际问题非常有用。应用部分由3章构成,分别介绍凸优化在解决逼近与拟合、统计估计和几何关系分析这三类实际问题中的应用。算法部分也由3章构成,依次介绍求解无约束凸优化模型、等式约束凸优化模型以及包含不等式约束的凸优化模型的经典数值方法,以及如何利用凸优化理论分析这些方法的收敛性质。
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