Turnpike phenomenon and symmetric optimization problems / / Alexander J. Zaslavski

• Record Nr.: UNISA996472038803316
• Autore: Zaslavski Alexander J.
• Pubbl/distr/stampa: Cham, Switzerland : , : Springer, , [2022]; ©2022
• ISBN: 9783030969738; 9783030969721
• Descrizione fisica: 1 online resource (339 pages)
• Collana: Springer Optimization and Its Applications ; ; v.190
• Disciplina: 519.6
• Soggetti: Mathematical optimization; Calculus of variations; Turnpike theory (Economics); Optimització matemàtica; Càlcul de variacions; Llibres electrònics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Intro -- Preface -- Contents -- 1 Introduction -- 1.1 Generic Existence of Solutions of Minimization Problems -- 1.2 Optimization Problems Arising in Crystallography -- 1.3 Symmetric Optimization Problems -- 1.4 Turnpike Property for Variational Problems -- 1.5 Variational Problems with Symmetric Integrands -- 1.6 Notation -- 1.7 Exercises -- 2 Symmetric Optimization Problems -- 2.1 A Generic Approach in Optimization -- 2.2 A Generic Variational Principle -- 2.3 The First Generic Result -- 2.4 The Second and Third Generic Results -- 2.5 Proofs of Theorems 2.5 and 2.6 -- 2.6 The Fourth Result -- 2.7 The Fifth Generic Result -- 2.8 Auxiliary Results for Theorems 2.14 and 2.15 -- 2.9 Proof of Theorems 2.14 and 2.15 -- 2.10 σ-Porous Sets in a Metric Space -- 2.11 A Variational Principle and Porosity -- 2.12 Well-Posedness and Porosity for Classes of Minimization Problems -- 2.13 An Auxiliary Result -- 2.14 A Well-Posedness Result -- 2.15 An Extension of Theorem 2.4 -- 2.16 Extensions of Theorems 2.5 and 2.6 -- 2.17 Extension of Theorem 2.10 -- 2.18 An Extension of Theorem ; 2.14 -- 3 Parametric Optimization -- 3.1 Generic Variational Principle -- 3.2 Concretization of the Hypothesis (H) -- 3.3 The First Generic Existence Results -- 3.4 The Second Generic Existence Result -- 4 Infinite Dimensional Control -- 4.1 Banach Space Valued Functions -- 4.2 Unbounded Operators -- 4.3 C0 Semigroup -- 4.4 Evolution Equations -- 4.5 C0 Groups -- 4.6 Admissible Control Operators -- 4.7 Examples -- 5 Symmetric Variational Problems -- 5.1 Preliminaries -- 5.2 The First Weak Turnpike Result -- 5.3 Auxiliary Results for the Turnpike Property -- 5.4 A Turnpike Result -- 5.5 The Second Weak Turnpike Result -- 5.6 The Space of Integrands -- 5.7 Auxiliary Results for Theorem 5.9 -- 5.8 Proof of Theorem 5.9 -- 5.9 Stability of the Weak Turnpike.; 5.10 Two Extensions of Theorem 5.9 -- 5.11 The Turnpike Phenomenon in the Regions Close to the Right End Points -- 6 Infinite Dimensional Optimal Control -- 6.1 Preliminaries -- 6.2 The First Turnpike Result -- 6.3 The Space of Integrands -- 6.4 The Turnpike Property -- 6.5 The Second Weak Turnpike Result -- 6.6 A Well-Posedness Result -- 6.7 Stability of the Turnpike Phenomenon -- 6.8 An Auxiliary Result for Theorem 6.11 -- 6.9 Proof of Theorem 6.11 -- 6.10 Stability of the Weak Turnpike Phenomenon -- 6.11 The First Extension of Theorem 6.11 -- 6.12 The Second Extension of Theorem 6.11 -- 6.13 The Turnpike Property in the Regions Close to the Right end Points -- 7 Optimization Problems Arising in Crystallography -- 7.1 Preliminaries -- 7.2 Auxiliary Results -- 7.3 A Basic Lemma -- 7.4 Proof of Theorem 7.2 -- 7.5 A Porosity Result -- 7.6 The Set MMr is Porous -- 7.7 Auxiliary Results -- 7.8 Proof of Theorem 7.11 -- 8 Discrete Dispersive Dynamical Systems -- 8.1 Dynamical Systems with a Lyapunov Function -- 8.2 Proof of Theorem 8.1 -- 8.3 Proofs of Propositions 8.2, 8.3, and 8.5 -- 8.4 Proof of Theorem 8.6 -- 8.5 Proof of Theorem 8.7 -- 8.6 Proof of Theorem 8.9 -- 8.7 The First Weak Turnpike Result -- 8.8 An Auxiliary Result -- 8.9 Proof of Theorem 8.10 -- 8.10 The Second Weak Turnpike Result -- 8.11 An Auxiliary Result -- 8.12 Proof of Theorem 8.12 -- 8.13 Stability Results -- 8.14 An Auxiliary Result -- 8.15 Proof of Theorem 8.14 -- 8.16 Proof of Theorem 8.15 -- References -- Index.