A Structure Exploiting Algorithm for Non-Smooth Semi-Linear Elliptic Optimal Control Problems

Olga Weiß(olga.weisshu-berlin.de)
Andrea Walther(andrea.walthermath.hu-berlin.de)
Stephan Schmidt(s.schmidthu-berlin.de)

Abstract: We investigate optimization problems with a non-smooth partial differential equation as constraint, where the non-smoothness is assumed to be caused by Nemytzkii operators generated by the functions abs, min and max. For the efficient as well as robust solution of such problems, we propose a new optimization method based on abs-linearization, i.e., a special handling of the non-smoothness with proficient exploitation of the non-smooth structure. The exploitation of the given data allows a targeted and optimal decomposition of the optimization problem in order to compute stationary points. This approach is able to solve the considered class of non-smooth optimization problems in comparably less Newton steps and additionally maintains reasonable convergence properties. Numerical results for non-smooth optimization problems illustrate the proposed approach and its performance.

Keywords: Non-Smooth Optimization; Compact Abs-Linearization; PDE Constrained Optimization; Non-Smooth PDE; Elliptic Optimal Control Problem

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 2: Infinite Dimensional Optimization

Citation: submitted 2020

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Entry Submitted: 12/14/2020
Entry Accepted: 12/14/2020
Entry Last Modified: 12/14/2020

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