Tuesday, 13:15 - 13:40 h, Room: H 0107

 

Manuel Jaraczewski
Interior point methods for a new class of minimum energy point systems on smooth manifolds

Coauthors: Marco Rozgic, Marcus Stiemer

 

Abstract:
Point systems with minimum discrete Riesz energy on smooth mani-folds are often considered as good interpolation and quadrature points. Their properties have intensively been studied, particularly for the sphere and for tori. However, these points do not optimally fast converge to the corresponding equilibrium distribution, since the continuous potential's singularity is poorly reproduced. We, hence, propose an alternative point system that avoids this problem and we provide a method for its numerical identification via constrained optimization with an interior point method. The key idea is dividing the points into two classes and considering them as vertices of a graph and its dual, respectively. Geometric relations between primal faces and dual vertices serve as constraints, which additionally stabilize the optimization procedure. Further, a prior global optimization method as usually applied for computing minimum discrete Riesz energy points can be avoided. Finally, for the new determined extreme points both approximation properties and efficient determinability are studied and compared to those of the minimum discrete Riesz energy points.

 

Talk 1 of the contributed session Tue.2.H 0107
"Methods for nonlinear optimization V" [...]
Cluster 16
"Nonlinear programming" [...]

 

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