Showing papers by "Andrea Walther published in 2019"
TL;DR: It is shown that the new method when started from within a compact level set generates a sequence of iterates whose cluster points are all Clarke stationary, which illustrates the capabilities of the proposed approach.
Abstract: We present an optimization method for Lipschitz continuous, piecewise smooth (PS) objective functions based on successive piecewise linearization. Since, in many realistic cases, nondifferentiabilities are caused by the occurrence of abs(), max(), and min(), we concentrate on these nonsmooth elemental functions. The method’s idea is to locate an optimum of a PS objective function by explicitly handling the kink structure at the level of piecewise linear models. This piecewise linearization can be generated in its abs-normal-form by minor extension of standard algorithmic, or automatic, differentiation tools. In this paper it is shown that the new method when started from within a compact level set generates a sequence of iterates whose cluster points are all Clarke stationary. Numerical results including comparisons with other nonsmooth optimization methods then illustrate the capabilities of the proposed approach.
13 citations
TL;DR: First order (KKT) and second order (second order sufficiency condition (SOSC) optimality conditions for functions defined byOptim.
Abstract: In the paper [Optim. Methods Softw., 31 (2016), pp. 904--930] we derived first order (KKT) and second order (second order sufficiency condition (SOSC)) optimality conditions for functions defined b...
12 citations
TL;DR: A new method is presented that computes a local minimizer of the proximal model objective, which is also known as criticality in nonsmooth optimization, and provides opportunities for structure exploitation like warm starts in the context of the nonlinear, outer loop.
Abstract: We previously derived first-order (KKT) and second-order (SOSC) optimality conditions for functions defined by evaluation programs involving smooth elementals and absolute values. For this class of...
8 citations
TL;DR: Functions defined by evaluation programs involving smooth elementals and absolute values as well as the max and min operators are piecewise smooth.
Abstract: Functions defined by evaluation programs involving smooth elementals and absolute values as well as the max and min operators are piecewise smooth. They can be approximated by piecewise linear func...
8 citations
TL;DR: In this article, a measurement set-up allows to calculate material parameters using one unique disc-shaped specimen with an optimised electrode topology, fitting material parameters can be found using an optimisation procedure.
Abstract: Abstract For its usage in simulation-based design processes a precise knowledge of the employed material properties is inevitable. In the case of piezoelectric ceramics, the provided material parameters often suffer from large uncertainties and even inconsistencies since the standardised measurement procedure needs several specimens to determine a single set of material parameters. In contrast, the presented measurement set-up allows to calculate material parameters using one unique disc-shaped specimen with an optimised electrode topology. Using an inverse problem approach, fitting material parameters can be found using an optimisation procedure.
2 citations