Quadratic Programming and Scalable Algorithms for Variational Inequalities

Zdeněek Dostál (), David Horák () and Dan Stefanica ()
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Zdeněek Dostál: FEI VŠB-Technical University Ostrava
David Horák: FEI VŠB-Technical University Ostrava
Dan Stefanica: City University of New York, Baruch College

A chapter in Numerical Mathematics and Advanced Applications, 2006, pp 62-78 from Springer

Abstract: Abstract We first review our recent results concerning optimal algorithms for the solution of bound and/or equality constrained quadratic programming problems. The unique feature of these algorithms is the rate of convergence in terms of bounds on the spectrum of the Hessian of the cost function. Then we combine these estimates with some results on the FETI method (FETI-DP, FETI and Total FETI) to get the convergence bounds that guarantee the scalability of the algorithms. i.e. asymptotically linear complexity and the time of solution inverse proportional to the number of processors. The results are confirmed by numerical experiments.

Keywords: Variational Inequality; Contact Problem; Domain Decomposition; Quadratic Programming Problem; Domain Decomposition Method (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1007/978-3-540-34288-5_4

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