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· 제목 : Optimal Control Problems Related to the Robinson-Solow-Srinivasan Model (Paperback)
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 응용수학
· ISBN : 9789811622540
· 쪽수 : 348쪽
· 출판일 : 2022-08-09
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 응용수학
· ISBN : 9789811622540
· 쪽수 : 348쪽
· 출판일 : 2022-08-09
목차
Chapter 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 Robinson-Solow-Srinivasan model
1.6. Overtaking optimal programs for the Robinson-Solow-Srinivasan model
1.7. Turnpike properties of the Robinson-Solow-Srinivasan model
Chapter 2. Good programs for infinite horizon optimal control problems
2.1. Preliminaries and the main results
2.2. Upper semicontinuity of cost functions
2.3 The nonstationary Robinson-Solow-Srinivasan 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. Problems with discounting
2.10. The Robinson-Solow-Srinivasan model with discounting
2.11. Auxiliary results for Theorem 2.23
2.12. Proof of Theorem 2.23
Chapter 3. One-dimensional concave Robinson-Solow-Srinivasan 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
Chapter 4. Autonomous nonconcave optimal control problems
4.1. Preliminaries
4.2. A controlability lemma
4.3. The turnpike property implies the asymptotic turnpike property
4.4. Auxiliary results
4.5. The asymptotic turnpike property implies the turnpike property
4.6. A weak turnpike property
4.7. A turnpike result
4.8. Auxiliary results for Theorem 4.11
4.9. Proof of Theorem 4.11
4.10. Stability results
4.11. A subclass of models
Chapter 5. Turnpike phenomenon for nonautonomous problems
5.1 Preliminaries
5.2. Turnpike properties
5.3. Examples
5.4. The turnpike property implies (P1) and (P2)
5.5. Auxiliary results
5.6. Completion of the proof of Theorem 5.2
5.7. A turnpike result
5.8. An auxiliary result for Theorem 5.8
5.9. Proof of Theorem 5.8
5.10. Stability results
5.11. Proof of Theorem 5.11
Chapter 6. Generic results
6.1. One-dimensional nonconcave Robinson-Solow-Srinivasan model
6.2. The 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 Theorem 6.10
Chapter 7. Turnpike phenomenon for a class of optimal control problems
7.1. Preliminaries and main results
7.2. Auxiliary results
7.3. Proof of Theorem 7.2
7.4. Proof of Theorem 7.3
7.5. Proofs of Theorems 7.4 and 7.5
7.7. The Robinson-Solow-Srinivasan model
7.8. A general model of economic dynamics
7.9. Equivalence of optimality criterions
7.10. Proof of Theorem 7.22
7.11 Weak turnpike results
7.12. Proof of Theorem 7.23
Chapter 8. Problems with perturbed objective functions
8.1 Preliminaries and main results
8.2. Auxiliary results
8.3 Proofs of Theorems 8.1 and 8.2
8.4. Proofs of Theorems 8.3 and 8.4
8.5. Problems with discounting
8.6. Auxiliary results for Theorems 8.10 and 8.11
8.7. Proof of Theorem 8.10
8.8. Proof of Theorem 8.11
8.9. Existence of overtaking optimal programs
Chapter 9. Stability of the turnpike phenomenon
9.1. Preliminaries and main results
9.2. Examples
9.3. Auxiliary results
9.4. Proof of Theorem 9.3
9.5. Proof of Theorem 9.4
9.6. Problems with discounting
9.7. Auxiliary results for Theorem 9.15
9.8. Proof of Theorem 9.15
