向量空间方法优化
Optimization by Vector Space Methods
David G. Luenberger · 初版 1968 年
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用几条几何原理统一优化领域：在各自领域中真正称得上经典的著作寥寥无几，但 David Luenberger 的 Optimization by Vector Space Methods 绝对实至名归。Luenberger 不仅清晰证明了优化领域的很大一部分可以通过线性向量空间理论的几条几何原理得到有效统一，而且他的方法还在远超出其最初应用的工程问题之外找到了广泛的应用场景。在其首次出版近 30 年后，本书
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……反正就这么个答案！至于剩下的，希尔伯特空间和巴拿赫空间又不会凭空消失！比如，要想看到 Hahn-Banach 定理的一大桌让人垂涎三尺的绝妙应用，翻翻 David G. Luenberger 的《Optimization by Vector Space Methods》就行，对于搞计算机的人可能遇到的很多问题，那本书都会是个很棒的方法库。> 你漏掉了图论和组合数学，这两门对 CS 来说都极其重要。关于……
…that answer anyway! For the rest, the Hilbert and Banach spaces won't go away! E.g., a huge dessert buffet of really finger lick'n good applications of the Hahn-Banach theorem is David G. Luenberger, 'Optimization by Vector Space Methods', and that book will be a nice source of methods for a lot that computing people might encounter. > You left out graph theory and combinatorics, both of which are extremely important to CS. For…
……正如我提到的，这似乎存在某种实用价值。关于能拿它做什么应用，在 D. Luenberger 的《Optimization by Vector Space Methods》里，基于 Hahn-Banach 定理等内容展开的应用简直像一长条甜品自助餐。真特么是个神器工具箱。只要搞出一个好应用，你就可以直接退休、给大学捐款、名字刻在教学楼上了。这里还有另一种可能：攻克整数线性规划问题……
…I mentioned it would seem that there is some practical value. For some of what can be done with applications, there is a long dessert buffet from the Hahn-Banach theorem and more in D. Luenberger, Optimization by Vector Space Methods. One heck of a toolkit. Make just one good application and retire, make a donation to a university, and get your name on a building. Here's another possibility: Attack integer linear programming problems…
……优秀技术写作的好范例。比如，科学方面，参考 Sears 等人写的大学普通物理教材。技术方面，看看 D. Knuth，哪怕只看他的《The TeXBook》。工程方面，看看比如 D. Luenberger 的《Optimization by Vector Space Methods》。数学方面，看看至少 50 年来任何一本备受推崇的大一微积分教材。也可以看看 W. Rudin 的书。我这里要探讨的核心问题是，技术写作……
…good examples of good technical writing. E.g., for science, see the freshman physics texts by Sears, etc. For technology, see D. Knuth, if only his The TeXBook. For engineering, see, say, D. Luenberger, Optimization by Vector Space Methods. For math, see, say, any of the more respected texts for freshman calculus going back at least 50 years. Also see the texts of W. Rudin. The core problem I am addressing here is that the technical writing…
……是个很深的话题，但通常一个相对简单的出路是通过正则条件概率，就像 Leo Breiman 在《Probability》（ISBN 0-89871-296-3，SIAM，费城）里写的那样。至于 David G. Luenberger 的《Optimization by Vector Space Methods》（John Wiley and Sons, Inc., 纽约），这本书对确定性最优控制、卡尔曼滤波，以及物理中“最小作用量”所需的数学，很可能给出了最平易近人的数学处理。……
…be a deep subject, but often a relatively simple way out is via regular conditional probabilities as in Leo Breiman, 'Probability', ISBN 0-89871-296-3, SIAM, Philadelphia. For David G. Luenberger, 'Optimization by Vector Space Methods', John Wiley and Sons, Inc., New York. this has likely the easiest mathematical treatment of deterministic optimal control and also Kalman filtering and also the math needed for 'least action' in physics.…
……答案就是：“高阶纯数和应用数学。”就这么简单。抱歉扎心了。比如在斯坦福，别管计算机系了，去查查 D. Luenberger，读读比如 David G. Luenberger 写的《Optimization by Vector Space Methods》（John Wiley and Sons, Inc., 纽约），里面大半都是靠 Hahn-Banach 定理吃香喝辣的妙用。再说一次，根本问题在于：只有极少数人能真正开创出成功的……
…Here is it: "Advanced pure and applied math.". Period. Sorry 'bout that. E.g., at Stanford, f'get about the Computer Science department, look up D. Luenberger, and study, say, David G. Luenberger, 'Optimization by Vector Space Methods', John Wiley and Sons, Inc., New York. which is fun and profit mostly from the Hahn-Banach theorem. Again, there is a fundamental problem: Only a tiny fraction of people can start really successful…
……由 E. Cinlar 的得意门生讲授的课程，也许我应该喜欢 Kollar 的课。抱歉，我真喜欢不起来——水平看着太次了。斯坦福有更好的质量吗？当然有，K. Chung、H. Royden、D. Luenberger（他的《Optimization by Vector Space Methods》就是一场写得极其优美、甚至可以说是典雅的一英里长应用数学甜品自助），还有 D. Knuth。至于“教你怎么写代码”的课，也就是软件入门材料，开什么玩笑！光会“写代码”……
…course by a star student of E. Cinlar, maybe I should like Kollar's course. Sorry, I didn't -- the quality looked too low. Better quality from Stanford? Sure, K. Chung, H. Royden, D. Luenberger (his 'Optimization by Vector Space Methods' is a beautifully, even elegantly, done one mile long applied math dessert buffet), D. Knuth. For courses in 'how to code', that is, introductory material in software, gotta be kidding! 'Coding' alone…