Nonlinear Optimization in IRn
II. Transversality, Flows, Parametric Aspects
Published in December 1986
Book
Paperback/Softback
302 pages
978-3-8204-9798-4 (ISBN)
Description
In this second volume we pay attention to three important subjects in nonlinear optimization. The first one concerns the dependence of an optimization problem on the problem data: stability, resp. sensitivity aspects are considered from both a local and global point of view. Since stability results are intimately related with some concepts of transversality, we treat transversality theory in detail. A second subject consists on one hand of gradients, the gradient differential equation and its use in the search for several local minima. On the other hand we treat the underlying differential equation for Newton's method for finding critical points of a function. Again, transversality plays a crucial role. Finally, we consider optimization problems depending on parameters (critical sets, bifurcation of the feasible set, etc.) The present volume is preceded by a first one in which we study manifolds with boundary and critical point theory (Morse theory) within the framework of nonlinear optimization.
Reviews / Votes
«This book gives many details on important subjects in nonlinear optimization from a differential-geometric point of view.» (H.Gfrerer, Zeitschrift für Operations Research)«The book is very clearly written and reflects in an impressive way the high competence of the authors who belong to the leading researchers in several fields treated here.» (R.Horst, Operations Research-Spektrum)
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Content
Contents: Stability theory for optimization problems, local and global sensitivity, (jet-)transversality theory, gradient differential equation, reflected gradients, the underlying differential equation for Newton's method, optimization problems depending on parameters.