凸优化导论
Introductory Lectures on Convex Optimization
Y. Nesterov · 初版 2003 年
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这是首部系统初级阐述 convex optimization 中 complexity theory 核心思想的著作。迄今为止，大部分内容仅见于专业期刊和研究专著中。本书涵盖了针对 smooth 和 non-smooth convex optimization 的最优方法以及 lower complexity bounds。另设专门章节探讨 polynomial-time interior-point methods。读者对象：本书适合工业工程师和经济学学者阅读。
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……给 Boyd 和 Vandenberghe 的建议。总体上我真的很喜欢 Boyd 的文风；他在 proximal algorithms 和 ADMM 方面合作写过几篇很棒的综述文章。另外再给两个建议：Nesterov 的《Introductory Lectures on Convex Optimization》。这本啃起来相当硬核，但我发现第一章的视角尤其启发人。Springer 好像出了一本更新的书，估计是这本书的扩展版。……
…suggestions for Boyd and Vandenberghe. I really like Boyd's writing in general; he has coauthored some good review articles on proximal algorithms and ADMM. A couple of other suggestions: Nesterov's Introductory Lectures on Convex Optimization. This one is pretty tough sledding, but I found the perspectives in the first chapter particularly to be enlightening. It seems like there's a newer Springer book which is probably an expansion on this.…
“基于梯度的优化与无导数 Lipschitz convex optimization 之间存在严格的复杂度差距”这结论几十年前就为人所知了。像 Nesterov 的《Introductory lectures on convex optimization》这种标准教材里都有讲。那个 AI 成果只是在一个相当小众的精度区间里证明了这个差距。
"A strict complexity gap between gradient-based and derivative-free Lipschitz convex optimization" has been known for decades. It's covered in standard textbooks like Nesterov's "Introductory lectures on convex optimization". That AI result is about establishing the gap in a fairly niche accuracy regime.