Optimization in Banach spaces / / Alexander J. Zaslavski

• Record Nr.: UNINA9910616207103321
• Autore: Zaslavski Alexander J.
• Pubbl/distr/stampa: Cham, Switzerland : , : Springer, , [2022]; ©2022
• ISBN: 9783031126444; 9783031126437
• Descrizione fisica: 1 online resource (132 pages)
• Collana: SpringerBriefs in Optimization
• Disciplina: 515.732
• Soggetti: Banach spaces; Mathematical optimization; Optimització matemàtica; Espais de Banach; 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 -- 1 Introduction -- 1.1 Notation -- 1.2 Constrained Optimization -- 1.3 Unconstrained Optimization -- 1.4 An Auxiliary Result -- 1.5 Proof of Theorem 1.1 -- 2 Convex Optimization -- 2.1 Preliminaries -- 2.2 A basic Lemma -- 2.3 Convergence Results -- 2.4 Proof of Theorem 2.2 -- 2.5 Proof of Theorem 2.3 -- 2.6 Proof of Theorem 2.4 -- 2.7 Proof of Theorem 2.5 -- 2.8 Proof of Theorem 2.6 -- 2.9 Proof of Theorem 2.7 -- 2.10 Proof of Theorem 2.8 -- 2.11 Proof of Theorem 2.9 -- 2.12 Proof of Theorem 2.10 -- 2.13 A Convergence Result with Estimations -- 2.14 An Auxiliary Result -- 2.15 Proof of Theorem 2.11 -- 3 Nonconvex Optimization -- 3.1 Preliminaries -- 3.2 Auxiliary Results -- 3.3 Convergence Results -- 3.4 Proofs of Theorems 3.5-3.9 -- 3.5 Proofs of Theorems 3.10-3.14 -- 3.6 Proof of Theorem 3.15 -- 3.7 A Convergence Result with Estimations -- 3.8 An Auxiliary Result -- 3.9 Proofs of Theorems 3.16 and 3.17 -- 4 Continuous Algorithms -- 4.1 Banach Space Valued Functions -- 4.2 Convex Problems -- 4.3 Proof of Theorem 4.5 -- 4.4 Proof of Theorem 4.6 -- 4.5 Proof of Theorem 4.7 -- 4.6 The First Convergence Result with Estimations -- 4.7 Nonconvex Optimization ; -- 4.8 Convergence Results -- 4.9 Proof of Theorem 4.11 -- 4.10 Proofs of Theorems 4.12 and 4.14 -- 4.11 Proof of Theorem 4.15 -- 4.12 Proof of Theorem 4.17 -- 4.13 The Second Convergence Result with Estimations -- References.