Torsten Bosse

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We address the problem of minimizing objectives from the class of piecewise 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)
y m i = vl i for i = 0, . . . ,m 1 Extraction . Here, x 2 X ✓ R denotes a vector of input variables, y = y(x) 2 R the corresponding output variables, and ' some smooth intermediate assignments from a library ⌘ +, , ⇤, /, p ·, exp, sin, cos, . . . . However, the smoothness assumption is violated in most real applications. For example, the evaluation routines(More)
Multigrid methods have been shown to be an efficient tool for solving partial differential equations. In this paper, the idea of a multigrid 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)
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)
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