Notice bibliographique
- Notice
Type(s) de contenu et mode(s) de consultation : Texte noté : électronique
Auteur(s) : Peypouquet, Juan
Titre(s) : Convex Optimization in Normed Spaces [Texte électronique] : Theory, Methods and Examples
Titre d'ensemble : Convex optimization in normed spaces / Peypouquet, Juan.
Édition : Online-Ausg
Publication : Cham : Springer International Publishing, 2015
Description matérielle : Online-Ressource (1 online resource (132 p.))
Collection : SpringerBriefs in Optimization ; v.0
EBL-Schweitzer
Note(s) : Description based upon print version of record
Foreword; Preface; Acknowledgments; Contents; Chapter1 Basic Functional Analysis;
1.1 Normed Spaces; 1.1.1 Bounded Linear Operators and Functionals, Topological Dual;
1.1.2 The Hahn-Banach Separation Theorem; 1.1.3 The Weak Topology; 1.1.4 Differential
Calculus; 1.2 Hilbert Spaces; 1.2.1 Basic Concepts, Properties and Examples; 1.2.2
Projection and Orthogonality; 1.2.3 Duality, Reflexivity and Weak Convergence; Chapter2
Existence of Minimizers; 2.1 Extended Real-Valued Functions; 2.2 Lower-Semicontinuity
and Minimization; 2.3 Minimizers of Convex Functions ; Chapter3 Convex Analysis and
Subdifferential Calculus3.1 Convexity and Continuity; 3.2 Convexity and Differentiability;
3.2.1 Directional Derivatives; 3.2.2 Characterizations of Convexity for Differentiable
Functions; 3.2.3 Lipschitz-Continuity of the Gradient; 3.3 Subgradients, Subdifferential
and Fermat's Rule; 3.4 Subdifferentiablility; 3.5 Basic Subdifferential Calculus Rules
and Applications; 3.5.1 Composition with a Linear Function: A Chain Rule; 3.5.2 Sum
of Convex Functions and the Moreau-Rockafellar Theorem; 3.5.3 Some Consequences; 3.5.4
Moreau-Yosida Regularization and Smoothing ; 3.6 The Fenchel Conjugate3.6.1 Main Properties
and Examples; 3.6.2 Fenchel-Rockafellar Duality; 3.6.3 The Biconjugate; 3.7 Optimality
Conditions for Constrained Problems; 3.7.1 Affine Constraints; 3.7.2 Nonlinear Constraints
and Lagrange Multipliers; Chapter4 Examples; 4.1 Norm of a Bounded Linear Functional;
4.2 Optimal Control and Calculus of Variations; 4.2.1 Controlled Systems; 4.2.2 Existence
of an Optimal Control; 4.2.3 The Linear-Quadratic Problem; 4.2.4 Calculus of Variations;
4.3 Some Elliptic Partial Differential Equations; 4.3.1 The Theorems of Stampacchia
and Lax-Milgram ; 4.3.2 Sobolev Spaces4.3.3 Poisson-Type Equations in H1 and W1,p;
4.4 Sparse Solutions for Underdetermined Systems of Equations; Chapter5 Problem-Solving
Strategies; 5.1 Combining Optimization and Discretization; 5.1.1 Recovering Solutions
for the Original Problem: Ritz's Method; 5.1.2 Building the Finite-Dimensional Approximations;
5.2 Iterative Procedures; 5.3 Problem Simplification; 5.3.1 Elimination of Constraints;
5.3.2 Splitting; Chapter6 Keynote Iterative Methods; 6.1 Steepest Descent Trajectories;
6.2 The Proximal Point Algorithm; 6.2.1 Basic Properties of Proximal Sequences ; 6.2.2
Strong Convergence and Finite-Time Termination6.2.3 Examples; 6.3 Gradient-Consistent
Algorithms; 6.3.1 The Gradient Method; 6.3.2 Newton's Method; 6.4 Some Comments on
Extensions and Variants; 6.4.1 Additive Splitting: Proximal and Gradient Methods;
6.4.2 Duality and Penalization; References; Index ; This work is intended to serve
as a guide for graduate students and researchers who wish to get acquainted with the
main theoretical and practical tools for the numerical minimization of convex functions
on Hilbert spaces. Therefore, it contains the main tools that are necessary to conduct
independent research on the topic. It is also a concise, easy-to-follow and self-contained
textbook, which may be useful for any researcher working on related fields, as well
as teachers giving graduate-level courses on the topic. It will contain a thorough
revision of the extant literature including both cl
Sujet(s) : Algorithmes
Optimisation mathématique
Mathématiques
Indice(s) Dewey :
510 (23e éd.) = Mathématiques ; 515.64 (23e éd.) = Calcul des variations
Identifiants, prix et caractéristiques : ISBN 9783319137100
Identifiant de la notice : ark:/12148/cb446783337
Notice n° :
FRBNF44678333
(notice reprise d'un réservoir extérieur)
