Lectures on Convex Optimization (Hardcover)

This book provides a comprehensive, modern introduction to convex optimization, a field that is becoming increasingly important in applied mathematics, economics and finance, engineering, and computer science, notably in data science and machine learning.

Written by a leading expert in the field, this book includes recent advances in the algorithmic theory of convex optimization, naturally complementing the existing literature. It contains a unified and rigorous presentation of the acceleration techniques for minimization schemes of first- and second-order. It provides readers with a full treatment of the smoothing technique, which has tremendously extended the abilities of gradient-type methods. Several powerful approaches in structural optimization, including optimization in relative scale and polynomial-time interior-point methods, are also discussed in detail.

Researchers in theoretical optimization as well as professionals working on optimization problems will find this book very useful. It presents many successful examples of how to develop very fast specialized minimization algorithms. Based on the author’s lectures, it can naturally serve as the basis for introductory and advanced courses in convex optimization for students in engineering, economics, computer science and mathematics.

這本書提供了一個全面且現代的凸優化入門，凸優化在應用數學、經濟學和金融學、工程學和計算機科學中變得越來越重要，特別是在數據科學和機器學習領域。

這本書由該領域的領先專家撰寫，包括凸優化算法理論的最新進展，自然地補充了現有的文獻。它提供了一個統一而嚴謹的加速技術介紹，適用於一階和二階最小化方案。它全面介紹了平滑技術，極大地擴展了梯度型方法的能力。書中還詳細討論了結構優化中的幾種強大方法，包括相對尺度優化和多項式時間內點法。

理論優化研究人員以及從事優化問題的專業人士將會發現這本書非常有用。它提供了許多成功的示例，展示了如何開發非常快速的專門最小化算法。基於作者的講座，它自然地可以作為工程、經濟學、計算機科學和數學專業學生的凸優化入門和高級課程的基礎。