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Efficient Techniques for Shape Optimization with Variational Inequalities Using Adjoints

In general, standard necessary optimality conditions cannot be formulated in a straightforward manner for semismooth shape optimization problems. In this paper, we consider shape optimization problems constrained by variational inequalities of the first kind, so-called obstacle-type problems. Under appropriate assumptions, we prove existence of adjoints for regularized problems and convergence to adjoints of the unregularized problem. Moreover, we derive shape derivatives for the regularized problem and prove convergence to a limit object. Based on this analysis, an efficient optimization algorithm is devised and tested numerically.

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Judul Seri

SIAM JOURNAL ON OPTIMIZATION; Vol.30 No.3 July-September 2020

No. Panggil

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Penerbit

: .,

Deskripsi Fisik

p. 1922 - 1953

Bahasa

English

ISBN/ISSN

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Klasifikasi

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Tipe Isi

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Tipe Media

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Tipe Pembawa

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Edisi

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Subjek

NUMERICAL METHODS
OBSTACLE PROBLEM
VARIATIONAL INEQUALITY
SHAPE OPTIMIZATION
SEMISMOOTH OPTIMIZATION
ADJOINT METHODS

Info Detail Spesifik

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Pernyataan Tanggungjawab

Daniel Luft, Volker H. Schulz, Kathrin Welker

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