Nonlinear Optimization in IRn: II. Transversality, Flows, Parametric Aspects

by Hubertus Th. Jongen, Frank Twilt

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 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.

302 pages, Paperback

First published December 31, 1983