Path-following interior point method: Theory and applications for the Stokes flow with a stick-slip boundary condition
•The improved path-following interior point method is proposed for minimization of quadratic functions subject to box and equality constraints.•Numerical experiments include large-scale problems arising from the TFETI domain decom- position method applied for solving the Stokes flow with the stick-s...
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| Published in | Advances in engineering software (1992) Vol. 129; pp. 35 - 43 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
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Elsevier Ltd
01.03.2019
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| Online Access | Get full text |
| ISSN | 0965-9978 |
| DOI | 10.1016/j.advengsoft.2018.06.010 |
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| Abstract | •The improved path-following interior point method is proposed for minimization of quadratic functions subject to box and equality constraints.•Numerical experiments include large-scale problems arising from the TFETI domain decom- position method applied for solving the Stokes flow with the stick-slip boundary condition.•The TFETI decomposition leads to the problems with the singular Hessian that is symmetric, positive definite only on the null space of the equality constraint matrix.•The inner linear systems are solved by the projected conjugate gradient method preconditioned by oblique projectors.
A path-following interior point method is proposed for minimization of quadratic functions subject to box and equality constraints. The problems with the singular Hessian that is symmetric, positive definite on the null space of the equality constraint matrix are considered. The inner linear systems are solved by the projected conjugate gradient method preconditioned by oblique projectors. Numerical experiments include large-scale problems arising from the TFETI domain decomposition method applied for solving the Stokes flow with the stick-slip boundary condition. |
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| AbstractList | •The improved path-following interior point method is proposed for minimization of quadratic functions subject to box and equality constraints.•Numerical experiments include large-scale problems arising from the TFETI domain decom- position method applied for solving the Stokes flow with the stick-slip boundary condition.•The TFETI decomposition leads to the problems with the singular Hessian that is symmetric, positive definite only on the null space of the equality constraint matrix.•The inner linear systems are solved by the projected conjugate gradient method preconditioned by oblique projectors.
A path-following interior point method is proposed for minimization of quadratic functions subject to box and equality constraints. The problems with the singular Hessian that is symmetric, positive definite on the null space of the equality constraint matrix are considered. The inner linear systems are solved by the projected conjugate gradient method preconditioned by oblique projectors. Numerical experiments include large-scale problems arising from the TFETI domain decomposition method applied for solving the Stokes flow with the stick-slip boundary condition. |
| Author | Kučera, Radek Brzobohatý, Tomáš Jarošová, Marta Šátek, Václav |
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| Keywords | 90C51 Stick-slip boundary condition Projected conjugate gradient method Path-following interior point method 65F35 76D07 Preconditioning Domain decomposition Stokes flow |
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| SubjectTerms | Domain decomposition Path-following interior point method Preconditioning Projected conjugate gradient method Stick-slip boundary condition Stokes flow |
| Title | Path-following interior point method: Theory and applications for the Stokes flow with a stick-slip boundary condition |
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