A structure exploiting algorithm for non-smooth semi-linear elliptic optimal control problems
| Autor: | Olga Weiß, Andrea Walther |
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| Jazyk: | English<br />French |
| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Surveys in Mathematics and its Applications, Vol 17 (2022), Pp 139-179 (2022) |
| Druh dokumentu: | article |
| ISSN: | 1843-7265 1842-6298 51672448 |
| Popis: | 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 very few Newton steps and additionally maintains reasonable convergence properties. Numerical results for non-smooth optimization problems illustrate the proposed approach and its performance. |
| Databáze: | Directory of Open Access Journals |
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