Nonlinear Optimization in IRN
I. Morse Theory, Chebyshev Approximation
Published on 31. December 1983
Book
Paperback/Softback
270 pages
978-3-8204-7903-4 (ISBN)
Description
In this first volume manifolds with boundary and critical point theory play an important role. We focus our attention to topological aspects in nonlinear optimization. In this way, we do not treat numerical and algorithmic features; however, we believe that the present work will provide a good insight into nonlinear phenomenae and that it will be helpful in order to device computational strategies towards global optimization. In order to underline the geometry of our analysis, many figures are included. In a second volume, we treat structural stability, transversality, (gradient-, Newton-)flows and parametric aspects.
Reviews / Votes
«It is an enrichment of the literature in the field of nonlinear optimization.» (M. Borchardt - K.-H. Elster, Optimization)More details
Content
Contents: This volume contains an introduction to manifolds with specially structured boundary, critical point theory and the connectedness structure of lower level sets of functions. Morse theory is treated within the framework of optimization theory, including a brief introduction to homology theory. Furthermore, some aspects of nonlinear Chebyshev approximation are presented, such as the reduction to functions of maximum type, optimality criteria and focal point theory.