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Description
  • We consider the problem of minimization of convex quadratic function subject to linear and quadratic constraints. Such minimizations arise from the finite element approximation of contact problems of linear elasticity with friction in 3D. We generalize the path-following (PF) variant of the interior point method that was proposed for solving linear programming problems. The main idea consists in applying the Newton iterations to solve equations in the (modified) system of the KKT conditions. The most expensive part of each iteration is the solution of an indefinite linear system. As the matrices are typically ill-conditioned, preconditioners are needed. Our preconditioners are optimal in the sense that condition numbers of the preconditioned matrices are bounded by a constant multiple of the condition number of the Hessian matrix of the given quadratic function.
  • We consider the problem of minimization of convex quadratic function subject to linear and quadratic constraints. Such minimizations arise from the finite element approximation of contact problems of linear elasticity with friction in 3D. We generalize the path-following (PF) variant of the interior point method that was proposed for solving linear programming problems. The main idea consists in applying the Newton iterations to solve equations in the (modified) system of the KKT conditions. The most expensive part of each iteration is the solution of an indefinite linear system. As the matrices are typically ill-conditioned, preconditioners are needed. Our preconditioners are optimal in the sense that condition numbers of the preconditioned matrices are bounded by a constant multiple of the condition number of the Hessian matrix of the given quadratic function. (en)
Title
  • Interior point method for 3D contact problems with fiction
  • Interior point method for 3D contact problems with fiction (en)
skos:prefLabel
  • Interior point method for 3D contact problems with fiction
  • Interior point method for 3D contact problems with fiction (en)
skos:notation
  • RIV/61989592:15310/12:33142073!RIV13-MSM-15310___
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  • S
http://linked.open...vai/riv/dodaniDat
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  • 142390
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  • RIV/61989592:15310/12:33142073
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  • contact problem with friction, interior point method, path-following algorithm, preconditioning (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...ontrolniKodProRIV
  • [56CE02BB27AF]
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  • Liberec
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  • Liberec
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  • SNA'12. Seminar on Numerical Analysis. Winter School.
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  • Kučera, Radek
  • Machalová, Jitka
  • Netuka, Horymír
  • Ženčák, Pavel
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number of pages
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  • Technická univerzita v Liberci
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  • 978-80-7372-821-2
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  • 15310
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