ISSN:
1573-2916
Keywords:
Global optimization
;
Gradient flow
;
Min-max graphs
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Let f be a smooth nondegenerate real valued function on a finite dimensional, compact and connected Riemannian manifold. The bipartite min-max graph Γ is defined as follows. Its nodes are formed by the set of local minima and the set of local maxima. Two nodes (a local minimum and a local maximum) are connected in Γ by means of an edge if some trajectory of the corresponding gradient flow connects them. Given a natural number k, we construct a function f such that the length of the shortest path in Γ between two specific local minima exceeds k. The latter construction is independent of the underlying Riemannian metric.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1026579317417
