Shape optimisation with nonsmooth cost functions: from theory to numerics

2016/03/27 by Sturm, Kevin
#35J62 #49J52 #49K20 #49K40 #49Q10 #49Q12 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1603.08235

Abstract

This paper is concerned with the study of a class of nonsmooth cost functions subject to a quasi-linear PDE in Lipschitz domains in dimension two. We derive the Eulerian semi-derivative of the cost function by employing the averaged adjoint approach and maximal elliptic regularity. Furthermore we characterise stationary points and show how to compute steepest descent direc- tions theoretically and practically. Finally, we present some numerical results for a simple toy problem and compare them with the smooth case. We also compare the convergence rates and obtain higher rates in the nonsmooth case.

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