Dynamic Programming

Name: Dynamic Programming
Brand: Princeton University Press
Price: 61.49 EUR
Availability: OnlineOnly

Richard E. Bellman(Autor*in)

Princeton University Press

1. Auflage

Erschienen am 10. August 2021

392 Seiten

E-Book

PDF mit Wasserzeichen-DRM

Systemvoraussetzungen

978-1-4008-3538-6 (ISBN)

61,49 €inkl. 7% MwSt.

Systemvoraussetzungen

für PDF mit Wasserzeichen-DRM

E-Book Einzellizenz

Als Download verfügbar

Beschreibung

Weitere Details

Weitere Ausgaben

Person

Inhalt

Cover Page
Half-title Page
Title Page
Copyright Page
Dedication Page
Contents
Introduction to the 2010 Edition
Preface
Chapter I. A Multi-Stage Allocation Process
1.1 Introduction
1.2 A multi-stage allocation process
1.3 Discussion
1.4 Functional equation approach
1.5 Discussion
1.6 A multi-dimensional maximization problem
1.7 A "smoothing" problem
1.8 Infinite stage approximation
1.9 Existence and uniqueness theorems
1.10 Successive approximations
1.11 Approximation in policy space
1.12 Properties of the solution-I: Convexity
1.13 Properties of the solution-II: Concavity
1.14 Properties of the solution-III: Concavity
1.15 An "ornery" example
1.16 A particular example-I
1.17 A particular example-II
1.18 Approximation and stability
1.19 Time-dependent processes
1.20 Multi-activity processes
1.21 Multi-dimensional structure theorems
1.22 Locating the unique maximum of a concave function
1.23 Continuity and memory
1.24 Stochastic allocation processes
1.25 Functional equations
1.26 Stieltjes integrals
Exercises and research problems
Bibliography and comments
Chapter II. A Stochastic Multi-Stage Decision Process
2.1 Introduction
2.2 Stochastic gold-mining
2.3 Enumerative treatment
2.4 Functional equation approach
2.5 Infinite stage approximation
2.6 Existence and uniqueness
2.7 Approximation in policy space and monotone convergence
2.8 The solution
2.9 Discussion
2.10 Some generalizations
2.11 The form off (x, y)
2.12 The problem for a finite number of stages
2.13 A three-choice problem
2.14 A stability theorem
Exercises and research problems
Bibliography and comments
Chapter III. The Structure of Dynamic Programming Processes
3.1 Introduction
3.2 Discussion of the two preceding processes
3.3 The principle of optimality
3.4 Mathematical formulation-I. A discrete deterministic process
3.5 Mathematical formulation-II. A discrete stochastic process
3.6 Mathematical formulation-III. A continuous deterministic process
3.7 Continuous stochastic processes
3.8 Generalizations
3.9 Causality and optimality
3.10 Approximation in policy space
Exercises and research problems
Bibliography and comments
Chapter IV. Existence and Uniqueness Theorems
4.1 Introduction
4.2 A fundamental inequality
4.3 Equations of type one
4.4 Equations of type two
4.5 Monotone convergence
4.6 Stability theorems
4.7 Some directions of generalization
4.8 An equation of the third type
4.9 An "optimal inventory" equation
Exercises and research problems
Bibliography and comments
Chapter V. The Optimal Inventory Equation
5.1 Introduction
5.2 Formulation of the general problem
A. Finite total time period
B. Unbounded time period-discounted cost
C. Unbounded time period-partially expendable items
D. Unbounded time period-one period lag in supply
E. Unbounded time period-two period lag
5.3 A simple observation
5.4 Constant stock level-preliminary discussion
5.5 Proportional cost-one-dimensional case
5.6 Proportional cost-multi-dimensional case
5.7 Finite time period
5.8 Finite time-multi-dimensional case
5.9 Non-proportional penalty cost-red tape
5.10 Particular cases
5.11 The form of the general solution
5.12 Fixed costs
5.13 Preliminaries to a discussion of more complicated policies
5.14 Unbounded process-one period time lag
5.15 Convex cost function-unbounded process
Exercises and research problems
Bibliography and comments
Chapter VI. Bottleneck Problems In Multi-Stage Production Processes
6.2 A general class of multi-stage production problems
6.3 Discussion of the preceding model
6.4 Functional equations
6.5 A continuous version
6.6 Notation
6.7 Dynamic programming formulation
6.8 The basic functional equation
6.9 The resultant nonlinear partial differential equation
6.10 Application of the partial differential equation
6.11 A particular example
6.12 A dual problem
6.13 Verification of the solution given in § 10
6.14 Computational solution
6.15 Nonlinear problems
Exercises and research problems
Bibliography and comments
Chapter VII. Bottleneck Problems: Examples
7.1 Introduction
7.2 Preliminaries
7.3 Delta-functions
7.4 The solution
7.5 The modified w solution
7.6 The equilibrium solution
7.7 A short-time w solution
7.8 Description of solution and proof
Bibliography and comments
Chapter VIII. A Continuous Stochastic Decision Process
8.1 Introduction
8.2 Continuous versions-I: A differential approach '
8.3 Continuous versions-II: An integral approach
8.4 Preliminary discussion
8.5 Mixing at a point
8.6 Reformulation of the gold-mining process
8.7 Derivation of the differential equations
8.8 The variational procedure
8.9 The behavior of Kt
8.10 The solution for T == oo
8.11 Solution for finite total time
8.12 The three-choice problem
8.13 Some lemmas and preliminary results
8.14 Mixed policies
8.15 The solution for infinite time, D & 0
8.16 D & 0
8.17 The caser = r4
8.18 Nonlinear utility-two-choice problem
Bibliography and comments
Chapter IX. A New Formalism in The Calculus Of Variations
9.1 Introduction
9.2 A new approach
9.3 Max [°° F(x,y)dt
9.4 Discussion
9.5 The two-dimensional case
9.6 Max (2 F(x, y)dt
9.7 Max F(x, y) dt under the constraint 0 &
y &C x
9.8 Computational solution
9.9 Discussion
9.10 An example
9.11 A discrete version
9.12 A convergence proof
9.13 Max (T F{x&yJ)dt
9.14 Generalization and discussion
9.15 Integral constraints
9.16 Further remarks concerning numerical solution
9.17 Eigenvalue problems
9.18 The first formulation
9.19 An approximate solution
9.20 Second formulation
9.21 Discrete approximations
9.22 Successive approximation
9.23 Monotone approximation
9.24 Uniqueness of solution
9.25 Minimum maximum deviation
Exercises and research problems
Bibliography and comments
Chapter X. Multi-Stage Games
10.1 Introduction
10.2 A single-stage discrete game
10.3 The min-max theorem
10.4 Continuous games
10.5 Finite resources
10.6 Games of survival
10.7 Pursuit games
10.8 General formulation
10.9 The principle of optimality and functional equations
10.10 More general process
10.11 A basic lemma
10.12 Existence and uniqueness
10.13 Proof of results
10.14 Alternate proof of existence
10.15 Successive approximations in general
10.16 Effectiveness of solution
10.17 Further results
10.18 One-sided min-max
10.19 Existence and uniqueness for games of survival
10.20 An approximation
10.21 Non-zero-sum games - games of survival
10.22 An approximate solution
10.23 Proof of the extended min-max theorem
10.24 A rationale for non-zero sum games
Exercises and research problems
Bibliography and comments
Chapter XI. Markovian Decision Processes
11.1 Introduction
11.2 Markovian decision processes
11.3 Notation
11.4 A lemma
11.5 Existence and uniqueness-I
11.6 Existence and uniqueness-II
11.7 Existence and uniqueness-III
11.8 The Riccati equation
11.9 Approximation in policy space
11.10 Discrete versions
11.11 The recurrence relation
11.12 Min-max
11.13 Generalization of a Von Neumann result
Exercises and research problems
Bibliography and comments
Index of applications
Name and subject index

Systemvoraussetzungen

Als PDF speichern Als Link merken