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Intro -- Preface -- Contents -- 1 Introduction -- 1.1 The Turnpike Phenomenon for Convex Discrete-TimeProblems -- 1.2 The Turnpike Phenomenon -- 1.3 Turnpike Results for Problems in Metric Spaces -- 1.4 The Robinson-Solow-Srinivasan Model -- 2 The Description of the Robinson-Solow-Srinivasan Model and Its Basic Properties -- 2.1 The Robinson-Solow-Srinivasan Model -- 2.2 A Golden-Rule Stock -- 2.3 Good Programs -- 2.4 The von Neumann Facet -- 3 Infinite Horizon Optimization -- 3.1 Overtaking Optimal Programs -- 3.2 Auxiliary Results for Theorems 3.1-3.3 -- 3.3 Proofs of Theorems 3.1 and 3.2 -- 3.4 Proof of Theorem 3.3 -- 3.5 Examples -- 3.6 Convergence Results -- 3.7 Proof of Theorem 3.9 -- 3.8 Auxiliary Results for Theorems 3.10 and 3.11 -- 3.9 Proofs of Theorems 3.10 and 3.11 -- 3.10 The Structure of Good Programs in the RSS Model -- 3.11 Proofs of Theorems 3.16-3.18 -- 4 Turnpike Results for the Robinson-Solow-Srinivasan Model -- 4.1 The Main Results -- 4.2 Auxiliary Results for Theorems 4.2 and 4.3 -- 4.3 Four Lemmas -- 4.4 Proof of Theorem 4.2 -- 4.5 Proof of Theorem 4.3 -- 4.6 Extensions of Theorem 4.3 -- 4.7 Proof of Theorem 4.16 -- 4.8 Stability Results -- 4.9 Proof of Theorem 4.27 -- 5 The Robinson-Solow-Srinivasan Model with a Nonconcave Utility Function -- 5.1 Good Programs -- 5.2 Auxiliary Results -- 5.3 Properties of the Function U -- 5.4 Proofs of Theorems 5.4, 5.5 and 5.8 -- 5.5 Proof of Proposition 5.7 -- 5.6 Proof of Theorem 5.9 -- 5.7 The RSS Model with Discounting -- 5.8 An Auxiliary Result for Theorem 5.18 -- 5.9 Proof of Theorem 5.18 -- 5.10 Weakly Agreeable Programs -- 5.11 Proof of Theorem 5.22 -- 5.12 Auxiliary Results -- 5.13 Proof of Theorem 5.23 -- 5.14 Proof of Theorem 5.24 -- 5.15 Weakly Maximal Programs -- 5.16 Proof of Theorem 5.27 -- 5.17 Proof of Theorem 5.28 -- 5.18 Proof of Theorem 5.29.

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.

Intro -- Preface -- Contents -- 1 Introduction -- 1.1 Convex Discrete-Time Problems -- 1.2 The Turnpike Phenomenon -- 2 Infinite Horizon Optimal Control Problems -- 2.1 The Forest Management Problem -- 2.2 Infinite Horizon Problems Without Discounting -- 2.3 Auxiliary Results -- 2.4 Proofs of Theorems 2.6 and 2.7 -- 2.5 Proof of Theorem 2.9 -- 2.6 Proof of Theorem 2.10 -- 2.7 Infinite Horizon Problems with Discounting -- 2.8 An Auxiliary Result for Theorem 2.13 -- 2.9 Proof of Theorem 2.13 -- 2.10 An Application to the Forest Management Problem -- 3 Turnpike Properties -- 3.1 Preliminaries and Main Results -- 3.2 Auxiliary Results -- 3.3 Proof of Theorem 3.2 -- 3.4 Proof of Theorem 3.3 -- 3.5 Proof of Theorem 3.4 -- 3.6 Proof of Theorem 3.5 -- 3.7 Proof of Theorem 3.6 -- 3.8 Stability Results -- 3.9 Agreeable Programs -- 4 Generic Turnpike Properties -- 4.1 Preliminaries -- 4.2 Equivalence of the Turnpike Properties -- 4.3 Generic Results -- 5 Structure of Solutions in the Regions Close to the Endpoints -- 5.1 Preliminaries -- 5.2 Lagrange Problems -- 5.3 An Auxiliary Result for Theorem 5.13 -- 5.4 Proof of Theorem 5.13 -- 5.5 The First Class of Bolza Problems -- 5.6 An Auxiliary Result for Theorem 5.15 -- 5.7 Proof of Theorem 5.15 -- 5.8 The Second Class of Bolza Problems -- 5.9 Auxiliary Results for Theorem 5.17 -- 5.10 Proof of Theorem 5.17 -- 6 Applications to the Forest Management Problem -- 6.1 Preliminaries -- 6.2 Auxiliary Results -- 6.3 Turnpike Results -- 6.4 Generic Results -- References -- Index.

"We analyze the asymptotic behavior of inexact infinite products of nonexpansive mappings, which take a nonempty closed subset of a complete metric space into the space, in the case where the errors are sufficiently small."

"The notion of porosity is well known in Optimization and Nonlinear Analysis. Its importance is brought out by the fact that the complement of a -porous subset of a complete pseudo-metric space is a residual set, while the existence of the latter is essential in many problems which apply the generic approach. Thus, under certain circumstances, some re nements of known results can be achieved by looking for porous sets. In 2001 Gabour, Reich and Zaslavski developed certain generic methods for solving stochastic feasibility problems. This topic was further investigated in 2021 by Barshad, Reich and Zaslavski, who provided more general results in the case of unbounded sets. In the present paper we introduce and examine new generic methods that deal with the aforesaid problems, in which, in contrast with previous studies, we consider sigma-porous sets instead of meager ones."