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A cubic regularization algorithm for nonconvex optimization in function space (in preparation)

  • We propose a cubic regularization algorithm that is constructed to deal with nonconvex minimization problems in function space. It allows for a flexible choice of the regularization term and thus accounts for the fact that in such problems one often has to deal with more than one norm. Global and local convergence results are established in a general framework. Moreover, several variants of step computations are compared. In the context of nonlinear elasticity it turns out the a cg method applied to an augmented Hessian is more robust than truncated cg.
Metadaten
Author:Anton Schiela
Document Type:ZIB-Report
Tag:nonconvex optimization; nonlinear elasticity; optimization in function space
MSC-Classification:49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Mxx Numerical methods [See also 90Cxx, 65Kxx] / 49M37 Methods of nonlinear programming type [See also 90C30, 65Kxx]
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Bxx Elastic materials / 74B20 Nonlinear elasticity
Date of first Publication:2012/04/03
Series (Serial Number):ZIB-Report (12-16)
ISSN:1438-0064
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