Torsten Bosse

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We address the problem of minimizing objectives from the class of piece-wise differentiable functions whose nonsmoothness can be encapsulated in the absolute value function. They possess local piecewise linear approximations with a discrepancy that can be bounded by a quadratic proximal term. This overestimating local model is continuous but generally(More)
The (multistep) one-shot method for design optimization problems has been successfully implemented for various applications. To this end, a slowly convergent primal fixed-point iteration of the state equation is augmented by an adjoint iteration and a corresponding preconditioned design update. In this paper we present a modification of the method that(More)
Overview Algorithmic di↵erentiation (AD) allows the ecient numerical computation of sensitivities for any mathematical function y = F (x), F : R n ! R m that is suciently smooth and given by a finite straight-line code. assumption is violated in most real applications. For example, the evaluation routines of many physical applications contain nonsmooth(More)
Multigrid methods have been shown to be an efficient tool for solving partial differential equations. In this paper, the idea of a multi-grid method for nonsmooth problems is presented based on techniques from piecewise linear differentiation. In detail, the original nonsmooth problem is approximated by a sequence of piecewise linear models, which can be(More)
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