最优过程的数学理论

Mathematical Theory of Optimal Processes

L. S. Pontryagin

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Hacker News 上怎么说

  • ……——而这本书探讨了它。这本书是一个很好的初级入门读物。看来德雷福斯是 R. Bellman 的学生。至于 L. S. 庞特里亚金、V. G. 博尔强斯基、R. V. 加姆克列利泽和 E. F. 米申科的《最佳过程的数学理论》(The Mathematical Theory of Optimal Processes,ISBN 0-470-69381-9,纽约 John Wiley & Sons 旗下 Interscience 出版社)。它当然是庞特里亚金极大值原理的主要来源,因此也狠狠踢了某些领域的屁股……

    …-- and this book treats it. The book is a good, elementary start. Apparently Dreyfus was a R. Bellman student. For L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mischenko, 'The Mathematical Theory of Optimal Processes', ISBN 0-470-69381-9, Interscience Publishers, John Wiley & Sons, New York. it was, of course, the main source of the Pontryagin maximum principle, and, thus, a swift kick in the back side for parts…

  • ……卢恩伯格的《向量空间方法在最优化中的应用》(Optimization by Vector Space Methods),我把它称作靠哈恩-巴拿赫定理名利双收的典范。更多的内容可能在 L. S. 庞特里亚金、V. G. 博尔强斯基、R. V. 加姆克列利泽和 E. F. 米申科的《最佳过程的数学理论》里,以及在 E. B. 李和 L. 马库斯的《最优控制理论基础》,还有迈克尔·阿森斯与彼得·L·法尔布的《最优控制:理论及其应用导论》中。有段时间我……

    …Luenberger, Optimization by Vector Space Methods. which I call fun and profit from the Hahn-Banach theorem. There may be more in L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mischenko, The Mathematical Theory of Optimal Processes. and in E. B. Lee and L. Markus, Foundations of Optimal Control Theory. and in Michael Athans and Peter L. Falb, Optimal Control: An Introduction to the Theory and Its Applications. At one time I…

  • ……理论头脑。恰恰相反,他亲身展示了这个问题的方方面面。在五十年代,他几乎从公众视野中消失,多年后带着列宁奖和《最佳过程的数学理论》归来。书中的例子包括“两个飞行物体”以及实现让它们近距离相遇的最佳解任务……显然你不可能单凭纯数学就拿到列宁奖。……

    …theoretical mind. On the contray, he illustrates in person the many aspects of the problem. During the fifties, he virtually vanished from public and came back years later with a Lenin prize and "The Mathematical Theory of Optimal Processes". Examples in there include 'two flying objects' and the task of an optimal solution for the problem to get them in close proximity... Obviously you don't receive a Lenin prize for pure mathematics. The…

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