Theory of extremal problems

Medientyp: E-Book

Titel: Theory of extremal problems

Weitere Titel: T@eorii︠a︡ ėkstremal nykh zadach <English>

Enthält: Front Cover; Theory of Extremal Problems; Copyright Page; CONTENTS; Preface; Basic notation; CHAPTER 0 INTRODUCTION. BACKGROUND MATERIAL; 0.1 Functional analysis; 0.2 Differential calculus; 0.3 Convex analysis; 0.4 Differential equations; CHAPTER 1 NECESSARY CONDITIONS FOR AN EXTREMUM; 1.1 Statements of the problems and formulations of basic theorems; 1.2 Smooth problems. The Lagrange multiplier rule; 1.3 Convex problems. Proof of the Kuhn-Tucker theorem; 1.4 Mixed problems. Proof of the extremal principle
CHAPTER 2 NECESSARY CONDITIONS FOR AN EXTREMUM IN THE CLASSICAL PROBLEMS OF THE CALCULUS OF VARIATIONS AND OPTIMAL CONTROL2.1 Statements of the problems; 2.2 Elementary derivation of necessary conditions for an extremum in simplest problems of the classical calculus of variations; 2.3 The Lagrange problem. The Euler-Lagrange equation; 2.4 The Pontrjagin maximum principle. Formulation and discussion; 2.5 Proof of the maximum principle; CHAPTER 3 ELEMENTS OF CONVEX ANALYSIS; 3.1 Convex sets and separation theorems; 3.2 Convex functions; 3.3 Conjugate functions. The Fenche1-Moreau theorem
3.4 Duality theorems3.5 Convex analysis in finite-dimensional spaces; CHAPTER 4 LOCAL CONVEX ANALYSIS; 4.1 Homogeneous functions and directional derivatives; 4.2 Subdifferentials. Basic theorems; 4.3 Cones of supporting functionals; 4.4 Locally convex functions; 4.5 The subdifferentials of certain functions; CHAPTER 5 LOCALLY CONVEX PROBLEMS AND THE MAXIMUM PRINCIPLE FOR PROBLEMS WITH PHASE CONSTRAINTS; 5.1 Locally convex problems; 5.2 Optimal control problems with phase constraints; 5.3 Proof of the maximum principle for problems with phase constraints; CHAPTER 6 SPECIAL PROBLEMS
6.1 Linear programming6.2 The theory of quadratic forms in Hilbert space; 6.3 Quadratic functionals in the classical caculus of variations; 6.4 Discrete optimal control problems; CHAPTER 7 SUFFICIENT CONDITIONS FOR AN EXTREMUM; 7.1 The perturbation method; 7.2 Smooth problems; 7.3 Convex problems; 7.4 Sufficient conditions for an extremum in the classical calculus of variations; CHAPTER 8 MEASURABLE MULTIMAPPINGS AND CONVEX ANALYSIS OF INTEGRAL FUNCTIONALS; 8.1 Multimappings and measurability; 8.2 Integration of multimappings; 8.3 Integral functionals
CHAPTER 9 EXISTENCE OF SOLUTIONS IN PROBLEMS OF THE CALCULUS OF VARIATIONS AND OPTIMAL CONTROL9.1 Semicontinuity of the functionals in the calculus of variations and the compactness of their level sets; 9.2 Theorems on the existence of solutions; 9.3 The convolution integral and linear problems; CHAPTER 10 APPLICATION OF THE THEORY TO SPECIFIC PROBLEMS; 10.1 Problems in geometric optics; 10.2 Young's inequality and Helly's theorem; 10.3 Optimal excitation of an oscillator; Problems; Bibliography; Subject Index;

Beteiligte: Tichomirov, Vladimir M. [Sonstige Person, Familie und Körperschaft]; Makowski, K. [Sonstige Person, Familie und Körperschaft]

Erschienen: Amsterdam; New York: North-Holland Pub. Co, 2010
Online-Ausg.: [S.l.]: HathiTrust Digital Library

Umfang: Online Ressource (xii, 460 pages); illustrations

Sprache: Englisch; Russisch

ISBN: 9780080875279; 0080875270; 9780444851673; 9781282754881

RVK-Notation: SK 660 : Variationsrechnung

Schlagwörter: Optimisation mathématique ; Maximums et minimums ; Calcul des variations ; Mathematical optimization ; Maxima and minima ; Calculus of variations ; Extremal problems (Mathematics) ; Mathematics ; MATHEMATICS ; Calculus ; MATHEMATICS ; Mathematical Analysis ; Optimierung ; Variationsrechnung ; Electronic books

Art der Reproduktion: Online-Ausg.

Hersteller der Reproduktion: [S.l.]: HathiTrust Digital Library

Reproduktionsnotiz: Online-Ausg. [S.l.] : HathiTrust Digital Library

Entstehung:

Anmerkungen: Includes bibliographical references (pages 443-456) and index. - Print version record
Print version record
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002

Beschreibung: Front Cover; Theory of Extremal Problems; Copyright Page; Preface; Basic notation; CONTENTS; CHAPTER 0 INTRODUCTION. BACKGROUND MATERIAL; CHAPTER 1 NECESSARY CONDITIONS FOR AN EXTREMUM; CHAPTER 2 NECESSARY CONDITIONS FOR AN EXTREMUM IN THE CLASSICAL PROBLEMS OF THE CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; CHAPTER 3 ELEMENTS OF CONVEX ANALYSIS; CHAPTER 4 LOCAL CONVEX ANALYSIS; CHAPTER 5 LOCALLY CONVEX PROBLEMS AND THE MAXIMUM PRINCIPLE FOR PROBLEMS WITH PHASE CONSTRAINTS; CHAPTER 6 SPECIAL PROBLEMS; CHAPTER 7 SUFFICIENT CONDITIONS FOR AN EXTREMUM

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