Title data
Schiela, Anton ; Stöcklein, Matthias:
Algorithms for Optimal Control of Elastic Contact Problems with Finite Strain.
University Bayreuth
,
2019
.  21 S.


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Project information
Project financing: 
Deutsche Forschungsgemeinschaft DFG grant SCHI 1379/21 within the priority programme SPP 1962 

Abstract
Optimal control of hyperelastic contact problems in the regime of finite strains combines various severe theoretical and algorithmic difficulties. Apart from being large scale, the main source of difficulties is the high nonlinearity and nonconvexity of the elastic energy functional which precludes uniqueness of solutions and simple local sensitivity results. In addition, the contact conditions add nonsmoothness to the overall problem. In this paper, we discuss algorithmic approaches to address these issues. In particular, the nonsmoothness is tackled by a pathfollowing approach, whose theoretical properties are reviewed. The subproblems are highly nonlinear optimal control problems, which can be solved by an affine invariant composite step method. For increased robustness and efficiency this method has to be adapted to the particular problem, taking into account its large scale nature, its function space structure and its nonconvexity.