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D. Horák^1,2, Z. Dostál^2,3, J. Kružík^2,1, A. Růžička^2,1 and B. Halfarová^2,1

¹Department of Applied Mathematics and Computational Sciences, Institute of Geonics of the Czech Academy of Sciences, Ostrava, Czech Republic
²Department of Applied Mathematics, VSB-Technical University of Ostrava, Ostrava, Czech Republic
³IT4Innovations National Supercomputing Center, VSB-Technical University of Ostrava, Ostrava, Czech Republic

doi:10.4203/ccc.8.5.1

D. Horák, Z. Dostál, J. Kružík, A. Růžička, B. Halfarová, "New Variant of the Semi-Monotonic Augmented Lagrangian Algorithm", in P. Iványi, J. Kruis, B.H.V. Topping, (Editors), "Proceedings of the Twelfth International Conference on Engineering Computational Technology", Civil-Comp Press, Edinburgh, UK, Online volume: CCC 8, Paper 5.1, 2024, doi:10.4203/ccc.8.5.1

Keywords: quadratic programming, augmented Lagrangian, Lagrange multipliers, FETI method, contact problem, equality constraint, SMALE.

Abstract

SMALE is an efficient algorithm for solving quadratic programming problems with simple bounds and linear equality constraints. There are two variants of this method: one updates the parameter for precision control of an inner solver by a factor less than one (the preferable variant, as it does not change the Hessian via penalty update), and the other updates the penalty by a factor greater than one (resulting in a lower number of outer iterations and fewer Hessian multiplications in the inner solver). We use the MPRGP algorithm as an inner solver for solving bound-constrained quadratic programming problems. We introduce a new theoretically supported variant that updates both these parameters: multiplying the penalty by a factor greater than one and multiplying the parameter for precision control for the MPRGP stopping criterion by the square root of this factor. The larger penalty accelerates the outer loop, while the larger parameter for precision control accelerates the inner solver. Numerical experiments with the Total-FETI method demonstrate the effectiveness of this new variant.

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Front Page Browse CCC CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Conferences ISSN 2753-3239 CCC: 8 PROCEEDINGS OF THE TWELFTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY Edited by: P. Iványi, J. Kruis and B.H.V. Topping Paper 5.1 New Variant of the Semi-Monotonic Augmented Lagrangian Algorithm D. Horák^1,2, Z. Dostál^2,3, J. Kružík^2,1, A. Růžička^2,1 and B. Halfarová^2,1 ¹Department of Applied Mathematics and Computational Sciences, Institute of Geonics of the Czech Academy of Sciences, Ostrava, Czech Republic ²Department of Applied Mathematics, VSB-Technical University of Ostrava, Ostrava, Czech Republic ³IT4Innovations National Supercomputing Center, VSB-Technical University of Ostrava, Ostrava, Czech Republic doi:10.4203/ccc.8.5.1 Full Bibliographic Reference for this paper D. Horák, Z. Dostál, J. Kružík, A. Růžička, B. Halfarová, "New Variant of the Semi-Monotonic Augmented Lagrangian Algorithm", in P. Iványi, J. Kruis, B.H.V. Topping, (Editors), "Proceedings of the Twelfth International Conference on Engineering Computational Technology", Civil-Comp Press, Edinburgh, UK, Online volume: CCC 8, Paper 5.1, 2024, doi:10.4203/ccc.8.5.1 Keywords: quadratic programming, augmented Lagrangian, Lagrange multipliers, FETI method, contact problem, equality constraint, SMALE. Abstract SMALE is an efficient algorithm for solving quadratic programming problems with simple bounds and linear equality constraints. There are two variants of this method: one updates the parameter for precision control of an inner solver by a factor less than one (the preferable variant, as it does not change the Hessian via penalty update), and the other updates the penalty by a factor greater than one (resulting in a lower number of outer iterations and fewer Hessian multiplications in the inner solver). We use the MPRGP algorithm as an inner solver for solving bound-constrained quadratic programming problems. We introduce a new theoretically supported variant that updates both these parameters: multiplying the penalty by a factor greater than one and multiplying the parameter for precision control for the MPRGP stopping criterion by the square root of this factor. The larger penalty accelerates the outer loop, while the larger parameter for precision control accelerates the inner solver. Numerical experiments with the Total-FETI method demonstrate the effectiveness of this new variant. download the full-text of this paper (PDF, 9 pages, 888 Kb) go to the previous paper go to the next paper return to the table of contents return to the volume description
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