非常经典，我们教材就用的这个！该版本非常清晰，强烈推荐！ Preface xi 1 Introduction 1 1.1 Mathematical optimization . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Least-squares and linear programming . . . . . . . . . . . . . . . . . . 4 1.3 Convex optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.4 Nonlinear optimization . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.5 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.6 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 I Theory 19 2 Convex sets 21 2.1 Affine and convex sets . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.2 Some important examples . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.3 Operations that preserve convexity . . . . . . . . . . . . . . . . . . . . 35 2.4 Generalized inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.5 Separating and supporting hyperplanes . . . . . . . . . . . . . . . . . . 46 2.6 Dual cones and generalized inequalities . . . . . . . . . . . . . . . . . . 51 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 3 Convex functions 67 3.1 Basic properties and examples . . . . . . . . . . . . . . . . . . . . . . 67 3.2 Operations that preserve convexity . . . . . . . . . . . . . . . . . . . . 79 3.3 The conjugate function . . . . . . . . . . . . . . . . . . . . . . . . . . 90 3.4 Quasiconvex functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 3.5 Log-concave and log-convex functions . . . . . . . . . . . . . . . . . . 104 3.6 Convexity with respect to generalized inequalities . . . . . . . . . . . . 108 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

convex optimization

boyd的凸优化书，包括了书，课后答案，ppt和王书宁的译本

凸优化Convex Optimization 中文+英文+代码+讲义+习题解答 高清+书签

《Convex Optimization》凸优化英文原版。作者：Stephen Boyd, Lieven Vandenberghe 。出版时间：2004。出版社： Cambridge University Press

凸优化的经典英文原版教材 Stephen Boyd & Lieven Vandenberghe编写

斯坦福的《凸优化》课程配套的求解凸优化问题的Matlab工具包。

Available for the first time in paperback, R. Tyrrell Rockafellar's classic study presents readers with a coherent branch of nonlinear mathematical analysis that is especially suited to the study of optimization problems. Rockafellar's theory differs from classical analysis in that differentiability assumptions are replaced by convexity assumptions. The topics treated in this volume include: systems of inequalities, the minimum or maximum of a convex function over a convex set, Lagrange multipliers, minimax theorems and duality, as well as basic results about the structure of convex sets and the continuity and differentiability of convex functions and saddle-functions. This book has firmly established a new and vital area not only for pure mathematics but also for applications to economics and engineering. A sound knowledge of linear algebra and introductory real analysis should provide readers with sufficient background for this book. There is also a guide for the reader who may be using the book as an introduction, indicating which parts are essential and which may be skipped on a first reading.

R. T. Rockafellar. 1970. Convex Analysis. Princeton University Press.

机器学习和凸优化领域大牛Yurii Nesterov 2018年的最新力作。经典凸优化书籍 Introductory Lectures on Convex Optimization: A Basic Course 的再版。原书也可从如下地址下载https://link.springer.com/book/10.1007/978-3-319-91578-4