Optimal control problems related to the Robinson-Solow-Srinivasan model

Optimal control problems related to the Robinson-Solow-Srinivasan model / Alexander J. Zaslavski.

This book is devoted to the study of classes of optimal control problems arising in economic growth theory, related to the Robinson-Solow-Srinivasan (RSS) model. The model was introduced in the 1960s by economists Joan Robinson, Robert Solow, and Thirukodikaval Nilakanta Srinivasan and was further s...

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Bibliographic Details
Main Author: Zaslavski, Alexander J. (Author)
Format: eBook
Language:English
Published: Singapore : Springer, [2021]
Series:Monographs in mathematical economics ; volume 4.
Subjects:
Mathematical optimization.
Economics, Mathematical.
Turnpike theory (Economics)
Economía matemática
Optimización matemática
Economics, Mathematical
Mathematical optimization
Online Access:Click for online access
Table of Contents:
  • Intro
  • Preface
  • Contents
  • 1 Introduction
  • 1.1 The Turnpike Phenomenon
  • 1.2 Nonconcave (Nonconvex) Problems
  • 1.3 Examples
  • 1.4 Stability of the Turnpike Phenomenon
  • 1.5 The RSS Model
  • 1.6 Overtaking Optimal Programs for the RSS Model
  • 1.7 Turnpike Properties of the RSS Model
  • 1.8 Concluding Remarks
  • 2 Infinite Horizon Nonautonomous Optimization Problems
  • 2.1 The Model Description and Main Results
  • 2.2 Upper Semicontinuity of Cost Functions
  • 2.3 The Nonstationary RSS Model
  • 2.4 Auxiliary Results for Theorems 2.4, 2.5 and 2.7
  • 2.5 Properties of the Function U
  • 2.6 Proof of Theorem 2.4
  • 2.7 Proof of Theorem 2.5
  • 2.8 Proof of Theorem 2.7
  • 2.9 Overtaking Optimal Programs
  • 2.10 Applications to the Nonstationary RSS Model
  • 2.11 Auxiliary Results for Theorem 2.23
  • 2.12 Proof of Theorem 2.23
  • 3 One-Dimensional Concave RSS Model
  • 3.1 Preliminaries and Main Results
  • 3.2 Auxiliary Results
  • 3.3 Proof of Theorem 3.14
  • 3.4 Stability Results
  • 3.5 Proof of Theorem 3.26
  • 4 Turnpike Properties for Autonomous Problems
  • 4.1 The Model Description and Main Results
  • 4.2 A Controllability Lemma
  • 4.3 TP Implies ATP
  • 4.4 Two Auxiliary Results
  • 4.5 ATP Implies TP
  • 4.6 A Weak Turnpike Result
  • 4.7 A Turnpike Result for Approximate Solutions
  • 4.8 Auxiliary Results for Theorem 4.11
  • 4.9 Proof of Theorem 4.11
  • 4.10 Stability of the Turnpike Phenomenon
  • 4.11 A Subclass of Models
  • 4.12 Auxiliary Results
  • 4.13 Proof of Theorem 4.20
  • 5 The Turnpike Phenomenon for Nonautonomous Problems
  • 5.1 Preliminaries
  • 5.2 A Turnpike Property
  • 5.3 Examples
  • 5.4 TP Implies (P1) and (P2)
  • 5.5 Auxiliary Results
  • 5.6 Completion of the Proof of Theorem 5.2
  • 5.7 A Turnpike Result for Approximate Solutions
  • 5.8 An Auxiliary Result for Theorem 5.8
  • 5.9 Proof of Theorem 5.8
  • 5.10 Stability of the Turnpike Phenomenon
  • 5.11 Proof of Theorem 5.11
  • 6 Generic Turnpike Results for the One-Dimensional RSS Model
  • 6.1 Preliminaries
  • 6.2 Main Results
  • 6.3 Auxiliary Results
  • 6.4 Auxiliary Results for Theorem 6.6
  • 6.5 Proof of Theorem 6.6
  • 6.6 Proof of Theorem6.10
  • 7 The Turnpike Phenomenon for the Robinson-Shinkai-Leontief Model
  • 7.1 The Model Description and Preliminaries
  • 7.2 Turnpike Results for a General Model
  • 7.3 Main Results
  • 7.4 Proofs of Propositions 7.5-7.7
  • 8 Discrete Dispersive Dynamical Systems
  • 8.1 Uniform Convergence to Global Attractors
  • 8.2 Proof of Proposition 8.1
  • 8.3 Proof of Theorem 8.2
  • 8.4 An Auxiliary Result
  • 8.5 Proofs of Theorems 8.3 and 8.4
  • 8.6 Examples
  • 8.7 Spaces of Set-Valued Mappings
  • 8.8 Attracting Sets
  • 8.9 Proof of Theorem 8.11
  • 8.10 Proof of Theorem 8.12
  • 8.11 Proof of Theorem 8.14
  • 8.12 Extensions
  • 8.13 Proof of Proposition 8.24 and Theorem 8.25
  • 8.14 Proof of Theorem 8.26
  • 8.15 Proof of Theorem 8.27
  • 8.16 Generic Results
  • 8.17 Dynamical Systems with a Lyapunov Function

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