Global Optimization: On Pathlengths in Min-Max Graphs |
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Authors: | HARALD GÜNZEL HUBERTUS TH. Jongen |
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Affiliation: | (1) Department of Mathematics (C ), Aachen University of Technology, Aachen, Germany |
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Abstract: | Let f be a smooth nondegenerate real valued function on a finite dimensional, compact and connected Riemannian manifold. The bipartite min-max graph 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 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 between two specific local minima exceeds k. The latter construction is independent of the underlying Riemannian metric. |
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Keywords: | Global optimization Gradient flow Min-max graphs |
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