Contributed Session Tue.2.H 0107

Tuesday, 13:15 - 14:45 h, Room: H 0107

Cluster 16: Nonlinear programming [...]

Methods for nonlinear optimization V

 

Chair: Marco Rozgic

 

 

Tuesday, 13:15 - 13:40 h, Room: H 0107, Talk 1

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.

 

 

Tuesday, 13:45 - 14:10 h, Room: H 0107, Talk 2

Marco Rozgic
Interior point methods for the optimization of technological forming processes

Coauthors: Robert Appel, Marcus Stiemer

 

Abstract:
Recent results in forming technology indicate that forming limits of classical quasi-static forming processes can be extended by combining them with fast impulse forming. However, in such combined processes, parameters have to be chosen carefully, to achieve an increase in formability. In previous works a gradient based optimization procedure as well as a simulation framework for the coupled process has been presented. The optimization procedure strongly depends on the linearization of the full coupled problem, which has to be completely simulated for gradient- and function- evaluation. In order to gain insight into the structure of the underlying optimization problem we analyse parameter identification an elastic deformation problem. Within this framework all needed derivative information is analytically computable and optimality conditions can be proved. This is used to perform systematic studies of properties and behaviour of the problem. We show that replacing derivative information with finite difference approximations requires additional constraints in order to retain physical feasibility. Finally we extend the developed scheme by introducing a plasticity model.

 

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