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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)
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)
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)
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