Optimization in Function Spaces: With Stability Considerations in Orlicz Spaces

ISBN-13: 9783110250206 / Angielski / Twarda / 2011 / 402 str.

Peter Kosmol; Dieter Ma1/4ller-Wichards

Opis

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 equationsaredeveloped 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 isprovided 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."

Recenzje

"[...] this is essentially a self-contained, interesting and well-written book, parts of it being suitable for undergraduate students with a good background in mathematical analysis, linear algebra and measure theory. The book also provides material for master's-level courses and for advanced research in nonlinear and functional analysis."
Constantin Zalinescu in: University of Michigan Mathematical Reviews 2012c

O autorze

Peter Kosmol, Christian Albrechts University, Kiel, Germany; Dieter Müller-Wichards, Hamburg University of Applied Sciences, Germany.