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Quadratic Programming and Scalable Algorithms for Variational Inequalities

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • Zdeněek Dostál

    (FEI VŠB-Technical University Ostrava)

  • David Horák

    (FEI VŠB-Technical University Ostrava)

  • Dan Stefanica

    (City University of New York, Baruch College)

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.

Suggested Citation

  • Zdeněek Dostál & David Horák & Dan Stefanica, 2006. "Quadratic Programming and Scalable Algorithms for Variational Inequalities," Springer Books, in: Alfredo Bermúdez de Castro & Dolores Gómez & Peregrina Quintela & Pilar Salgado (ed.), Numerical Mathematics and Advanced Applications, pages 62-78, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-34288-5_4
    DOI: 10.1007/978-3-540-34288-5_4
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