On the solution of convex QPQC problems with elliptic and other separable constraints with strong curvature

The paper deals with an effective implementation of some algorithms for the solution of convex QPQC problems with elliptic and other separable constraints with strong curvature. Here we discuss robust quantitative refinement of the Karush–Kuhn–Tucker conditions, extend existing results on the decrea...

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Bibliographic Details
Published in:Applied mathematics and computation 2014-11, Vol.247, p.848-864
Main Authors: Bouchala, Jiří, Dostál, Zdeněk, Kozubek, Tomáš, Pospíšil, Lukáš, Vodstrčil, Petr
Format: Article
Language:English
Subjects:
Algorithms
Contact
Convergence
Coulomb friction
Curvature
Elliptic constraints
Inequalities
Mathematical analysis
Mathematical models
Orthotropic friction
Precision control
QPQC with separable constraints
Rate of convergence
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Summary:The paper deals with an effective implementation of some algorithms for the solution of convex QPQC problems with elliptic and other separable constraints with strong curvature. Here we discuss robust quantitative refinement of the Karush–Kuhn–Tucker conditions, extend existing results on the decrease of the cost function along the projected gradient path to separable constraints with elliptic components, and plug them into the existing algorithms for the solution of the QPQC problems with R-linear rate of convergence in the bounds on the spectrum. The results are then extended to the problems with separable inequality and linear equality constraints. The performance of the algorithms is demonstrated on the solution of a problem of two cantilever beams in mutual contact with orthotropic Tresca and Coulomb friction discretized by up to one and half million nodal variables.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2014.09.044