Dynamic Programming

This book, first published in 1996, introduces students to optimization theory and its use in economics and allied disciplines. The first of its three parts examines the existence of solutions to optimization problems in Rn, and how these solutions may be identified. The second part explores how solutions to optimization problems change with changes in the underlying parameters, and the last part provides an extensive description of the fundamental principles of finite- and infinite-horizon dynamic programming. Each chapter contains a number of detailed examples explaining both the theory and its applications for first-year master's and graduate students. 'Cookbook' procedures are accompanied by a discussion of when such methods are guaranteed to be successful, and, equally importantly, when they could fail. Each result in the main body of the text is also accompanied by a complete proof. A preliminary chapter and three appendices are designed to keep the book mathematically self-conta

This book presents a coherent and systematic exposition of the mathematical theory of the problems of optimization and stability. Both of these are topics central to economic analysis since the latter is so much concerned with the optimizing behaviour of economic agents and the stability of the interaction processes to which this gives rise. The topics covered include convexity, mathematical programming, fixed point theorems, comparative static analysis and duality, the stability of dynamic systems, the calculus of variations and optimal control theory. The authors present a more detailed and wide-ranging discussion of these topics than is to be found in the few books which attempt a similar coverage. Although the text deals with fairly advanced material, the mathematical prerequisites are minimised by the inclusion of an integrated mathematical review designed to make the text self-contained and accessible to the reader with only an elementary knowledge of calculus and linear algebra.

動態規劃(Dynamic Programming，DP；簡稱動規)在算法競賽中佔據極其重要的位置，也是初學者在剛接觸算法設計時覺得難以理解的知識點。簡單來說，動態規劃是一種用來解決最優化問題的算法思想，將一個複雜的問題分解成若干個子問題，通過綜合子問題的最優解來得到原問題的最優解，通常適用於解決有重疊子問題和最優子結構性質的問題。為了幫助初學者理解動態規劃，本書直接以各類競賽真題入手，全面細緻地介紹算法競賽中經常用到的各類動態規劃算法模型。為了讀者能更深刻地理解和掌握其算法思想內涵，本書精挑細選、由淺入深地安排了相關習題。

A new edition of the essential text and professional reference, with substantial newmaterial on such topics as vEB trees, multithreaded algorithms, dynamic programming, and edge-baseflow.

This book brings an overview of the necessary notions related to Lp-stability, impulsive delayed systems, switched systems, approximate dynamic programming, reinforcement learning, Markov processes, e

本書從資本調整成本視角出發，利用動態規劃（Dynamic Programming）貝爾曼（Bellman）方程研究企業的跨期最優化投資行為，這為微觀企業的投資動態行為提供了統一的研究框架，大大便利了企業投資的相關研究。 由於影響企業投資的成因有來自於企業外部的因素（稱之為外生性因素）和來自於企業內部的因素（稱之為內生性因素），絕大多數情況下外生性因素和內生性因素對企業投資的各自影響無法進行清晰的分割。為了測度某一因素對企業投資的動態影響，本書將影響投資的因素嵌入到動態規劃貝爾曼方程中，再通過反事實推斷分析方法來揭示該因素對企業投資的動態影響大小，顯然與簡約式計量模型相比，動態規劃方法具有明顯優勢。利用動態規劃方法來研究經濟學問題並不常見，主要原因在於，動態規劃一般都沒有明確的閉式解，通常利用值函數迭代或策略函數迭代來求解，所以計算成本往往較高。同時，對於模型參數的估計也不能採用常規的參數估計方法如最小二乘估計（OLS）或極大似然估計（ML）等，而要採用矩估計方法來估計模型的未知參數，因此模型估計難度較大且計算成本較高。