49M37 Methods of nonlinear programming type [See also 90C30, 65Kxx]
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A cubic regularization algorithm for nonconvex optimization in function space (in preparation)
(2012)
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.