Moreau–Yosida regularization in shape optimization with geometric constraints

Moritz Keuthen () and Michael Ulbrich

Computational Optimization and Applications, 2015, vol. 62, issue 1, 216 pages

Abstract: In the context of shape optimization with geometric constraints we employ the method of mappings (perturbation of identity) to obtain an optimal control problem with a nonlinear state equation on a fixed reference domain. The Lagrange multiplier associated with the geometric shape constraint has a low regularity (similar to state constrained problems), which we circumvent by penalization and a continuation scheme. We employ a Moreau–Yosida-type regularization and assume a second-order condition to hold. The regularized problems can then be solved with a semismooth Newton method and we study the properties of the regularized solutions and the rate of convergence towards a solution of the original problem. A model for the value function in the spirit of Hintermüller and Kunisch (SIAM J Control Optim 45(4): 1198–1221, 2006 ) is introduced and used in an update strategy for the regularization parameter. The theoretical findings are supported by numerical tests. Copyright Springer Science+Business Media New York 2015

Keywords: Shape optimization; Moreau–Yosida regularization; Method of mappings; Semismooth newton; Geometric constraints (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10589-014-9661-0

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