| Description |
1 online resource (xiv, 388 pages) : illustrations. |
| Physical Medium |
polychrome |
| Description |
text file |
| Series |
De Gruyter series in nonlinear analysis and applications,
0941-813X ;
13
|
|
De Gruyter series in nonlinear analysis and applications ; 13.
0941-813X
|
| Bibliography |
Includes bibliographical references and index. |
| Summary |
This is an essentially self-contained book on the theory of convex functions and convex optimization in Banach spaces, with a special interest in Orlicz spaces. Approximate algorithms based on the stability principles and the solution of the corresponding nonlinear equations are developed in this text. A synopsis of the geometry of Banach spaces, aspects of stability and the duality of different levels of differentiability and convexity is developed. And it is provided a novel approach to the fundamental theorems of Variational Calculus based on the principle of pointwise minimization of the Lagrangian on the one hand and convexification by quadratic supplements using the classical Legendre-Ricatti equation on the other. The reader should be familiar with the concepts of mathematical analysis and linear algebra. Some awareness of the principles of measure theory will turn out to be helpful. The book is suitable for students of the second half of undergraduate studies, and it provides a rich set of material for a master course on linear and nonlinear functional analysis. Additionally it offers novel aspects at the advanced level. |
| Contents |
Preface; Contents; 1 Approximation in Orlicz Spaces; 2 Polya Algorithms in Orlicz Spaces; 3 Convex Sets and Convex Functions; 4 Numerical Treatment of Non-linear Equations and Optimization Problems; 5 Stability and Two-stage Optimization Problems; 6 Orlicz Spaces; 7 Orlicz Norm and Duality; 8 Differentiability and Convexity in Orlicz Spaces; 9 Variational Calculus; Bibliography; List of Symbols; Index. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Stability -- Mathematical models.
|
|
Stability -- Mathematical models. |
|
Stability. |
|
Mathematical optimization.
|
|
Mathematical optimization. |
|
Orlicz spaces.
|
|
Orlicz spaces. |
| Genre/Form |
Electronic books.
|
| Added Author |
Müller-Wichards, D. (Dieter), 1946-
|
| Other Form: |
Print version: Kosmol, Peter. Optimization in function spaces. Berlin ; New York : De Gruyter, 2011 (DLC) 2010036123 |
| ISBN |
9783110250213 (electronic book) |
|
3110250217 (electronic book) |
|
1283166348 |
|
9781283166348 |
|
9783110250206 (alkaline paper) |
|
