03076nam 2200517 450 991061620710332120231110220459.09783031126444(electronic bk.)9783031126437(MiAaPQ)EBC7102365(Au-PeEL)EBL7102365(CKB)24950564900041(PPN)26495565X(EXLCZ)992495056490004120230226d2022 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierOptimization in Banach spaces /Alexander J. ZaslavskiCham, Switzerland :Springer,[2022]©20221 online resource (132 pages)SpringerBriefs in Optimization Print version: Zaslavski, Alexander J. Optimization in Banach Spaces Cham : Springer International Publishing AG,c2022 9783031126437 Includes bibliographical references and index.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.SpringerBriefs in Optimization Banach spacesMathematical optimizationOptimització matemàticathubEspais de BanachthubLlibres electrònicsthubBanach spaces.Mathematical optimization.Optimització matemàticaEspais de Banach515.732Zaslavski Alexander J.721713MiAaPQMiAaPQMiAaPQ9910616207103321Optimization in Banach Spaces2920192UNINA