Journal
OPTIMIZATION METHODS & SOFTWARE
Volume 22, Issue 3, Pages 413-431Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/10556780600605129
Keywords
affine conjugate Newton methods; nonconvex minimization; nonlinear elastomechanics; cranio-maxillofacial surgery
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The paper extends affine conjugate Newton methods from convex to nonconvex minimization, with particular emphasis on PDE problems originating from compressible hyperelasticity. On the basis of well-known schemes from finite dimensional nonlinear optimization, three different algorithmic variants are worked out in a function space setting, which permits an adaptive multilevel finite element implementation. These algorithms are tested on two well-known 3D test problems and a real-life example from surgical operation planning.
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