Optimal Control Problems Related to the Robinson-Solow-Srinivasan Model

Chapter 1. Introduction1.1 The turnpike phenomenon1.2. Nonconcave (nonconvex) problems1.3. Examples1.4. Stability of the turnpike phenomenon1.5 The Robinson-Solow-Srinivasan model1.6. Overtaking optimal programs for the Robinson-Solow-Srinivasan model1.7. Turnpike properties of the Robinson-Solow-Srinivasan modelChapter 2. Good programs for infinite horizon optimal control problems2.1. Preliminaries and the main results2.2. Upper semicontinuity of cost functions2.3 The nonstationary Robinson-Solow-Srinivasan model2.4. Auxiliary results for Theorems 2.4, 2.5 and 2.72.5. Properties of the function $U$2.6. Proof of Theorem 2.42.7. Proof of Theorem 2.52.8. Proof of Theorem 2.72.9. Problems with discounting2.10. The Robinson-Solow-Srinivasan model with discounting2.11. Auxiliary results for Theorem 2.232.12. Proof of Theorem 2.23Chapter 3. One-dimensional concave Robinson-Solow-Srinivasan model3.1. Preliminaries and main results3.2. Auxiliary results3.3. Proof of Theorem 3.143.4. Stability results3.5. Proof of Theorem 3.26Chapter 4. Autonomous nonconcave optimal control problems4.1. Preliminaries4.2. A controlability lemma4.3. The turnpike property implies the asymptotic turnpike property4.4. Auxiliary results4.5. The asymptotic turnpike property implies the turnpike property4.6. A weak turnpike property4.7. A turnpike result4.8. Auxiliary results for Theorem 4.114.9. Proof of Theorem 4.114.10. Stability results4.11. A subclass of modelsChapter 5. Turnpike phenomenon for nonautonomous problems5.1 Preliminaries5.2. Turnpike properties5.3. Examples5.4. The turnpike property implies (P1) and (P2)5.5. Auxiliary results5.6. Completion of the proof of Theorem 5.25.7. A turnpike result5.8. An auxiliary result for Theorem 5.85.9. Proof of Theorem 5.8 5.10. Stability results5.11. Proof of Theorem 5.11Chapter 6. Generic results6.1. One-dimensional nonconcave Robinson-Solow-Srinivasan model6.2. The main results6.3. Auxiliary results6.4. Auxiliary results for Theorem 6.6.6.5. Proof of Theorem 6.66.6. Proof of Theorem 6.10Chapter 7. Turnpike phenomenon for a class of optimal control problems7.1. Preliminaries and main results7.2. Auxiliary results7.3. Proof of Theorem 7.27.4. Proof of Theorem 7.37.5. Proofs of Theorems 7.4 and 7.57.7. The Robinson-Solow-Srinivasan model7.8. A general model of economic dynamics7.9. Equivalence of optimality criterions7.10. Proof of Theorem 7.227.11 Weak turnpike results7.12. Proof of Theorem 7.23Chapter 8. Problems with perturbed objective functions8.1 Preliminaries and main results8.2. Auxiliary results8.3 Proofs of Theorems 8.1 and 8.28.4. Proofs of Theorems 8.3 and 8.48.5. Problems with discounting8.6. Auxiliary results for Theorems 8.10 and 8.118.7. Proof of Theorem 8.108.8. Proof of Theorem 8.118.9. Existence of overtaking optimal programsChapter 9. Stability of the turnpike phenomenon9.1. Preliminaries and main results9.2. Examples9.3. Auxiliary results9.4. Proof of Theorem 9.39.5. Proof of Theorem 9.49.6. Problems with discounting9.