Abstract
Two proportionality based gradient methods for the solution of large convex bound constrained quadratic programming problems, MPRGP (Modified Proportioning with Reduced Gradient Projections) and P2GP (Proportionality-based Two-phase Gradient Projection) are presented and applied to the solution of auxiliary problems in the inner loop of an augmented lagrangian algorithm called SMALBE (Semi-monotonic Augmented Lagrangian for Bound and Equality constraints). The SMALBE algorithm is used to generate the Lagrange multipliers for the equality constraints. The performance of the algorithms is tested on the solution of the discretized contact problems by means of TFETI (Total Finite Element Tearing and Interconnecting).
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Acknowledgement
This work was supported by The Ministry of Education, Youth and Sports from the National Programme of Sustainability (NPS II) project “IT4Innovations excellence in science - LQ1602” and by the IT4Innovations infrastructure which is supported from the Large Infrastructures for Research, Experimental Development and Innovations project “IT4Innovations National Supercomputing Center - LM2015070”. The work was partially supported by Gruppo Nazionale per il Calcolo Scientifico - Istituto Nazionale di Alta Matematica (GNCS-INdAM).
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Dostál, Z., Toraldo, G., Viola, M., Vlach, O. (2018). Proportionality-Based Gradient Methods with Applications in Contact Mechanics. In: Kozubek, T., et al. High Performance Computing in Science and Engineering. HPCSE 2017. Lecture Notes in Computer Science(), vol 11087. Springer, Cham. https://doi.org/10.1007/978-3-319-97136-0_4
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