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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 112
PROCEEDINGS OF THE SIXTH INTERNATIONAL CONFERENCE ON PARALLEL, DISTRIBUTED, GPU AND CLOUD COMPUTING FOR ENGINEERING
Edited by: P. Iványi and B.H.V. Topping
Paper 18

Choosing optimal expansion step-length of MPRGP algorithm

D. Horak 1,2, J. Kruzik 1,2, M. Pecha 1,2, V. Hapla 1,3 and M. Cermak 1,2,4,5

1Department of Applied Mathematics, FEEIC, VSB-TU Ostrava, Ostrava, Czech Republic
2Institute of Geonics of the Czech Academy of Sciences, Ostrava, Czech Republic
3Department of Earth Sciences, ETH Zurich, Zurich, Switzerland
4Department ofMathematics, Faculty of Civil Engineering, VSB-TU Ostrava, Ostrava, Czech Republic
5ENET Centre, VSB-TU Ostrava, Ostrava, Czech Republic

Full Bibliographic Reference for this paper
D. Horak, J. Kruzik, M. Pecha, V. Hapla, M. Cermak, "Choosing optimal expansion step-length of MPRGP algorithm", in P. Iványi, B.H.V. Topping, (Editors), "Proceedings of the Sixth International Conference on Parallel, Distributed, GPU and Cloud Computing for Engineering", Civil-Comp Press, Stirlingshire, UK, Paper 18, 2019. doi:10.4203/ccp.112.18
Keywords: MPRGP, active set, expansion step, PERMON..

Summary
PERMON (Parallel, Efficient, Robust, Modular, Object-oriented, Numerical) is a scalable software toolbox for the solution of the quadratic programming (QP) problems. It is based on PETSc, and it follows its highly successful design.

QP problems arise in various disciplines including elasto-plasticity, contact problems with friction, shape optimization, vehicle routing problems, support vector machines, medical imaging, climate modelling, least-squares regression, data fitting, data mining, control systems and many others.

The main functionality is contained in the PermonQP module. It provides a framework for the solution of QP problems. It includes data structures, transformations (e.g. dualization), algorithms, and supporting functions for QP. PermonQP can use all solvers and interfaces to the external packages provided by PETSc as well as our implementations of algorithms such as SMALBE (SemiMonotonic Augmented Lagrangian algorithm for Bound and Equality constraints) or MPRGP (Modified Proportioning with Reduced Gradient Projections).

Among the presented QP applications belongs the solution of a model 3D linear elasticity contact problem and its novel Projector-avoiding variant implemented in PermonFLLOP. The classical (T)FETI operator contains two applications of the corse problem (CP) projector. The solution of CP represents a bottleneck in the FETI methods parallelization. The main idea of the Projector-avoiding TFETI method lays in a cheap way to project this generalized inverse onto the range of the stiffness matrix. This projection results in the Moore-Penrose pseudoinverse that is much better conditioned than the classical TFETI operator. We obtain not only a system with improved eigenvalue distribution, but we also do not need to multiply this matrix by CP projectors, i.e. we avoid some of the CP projector applications. Our tests of the Projector-avoiding method show about 1.7 speedup over standard TFETI on problems with more than 1.25 billion of unknowns computed on up to 15,625 cores.

Another application will be machine learning using linear Support Vector Machines (SVMs) implemented in the PermonSVMmodule. The quality of the solution, as well as the scalability of the QP solvers, will be demonstrated on benchmarks from the LIBSVMcollection and other datasets.

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