Convergence Rate Analysis of a Multiplicative Schwarz Method for Variational Inequalities

@article{Badea2003ConvergenceRA,
  title={Convergence Rate Analysis of a Multiplicative Schwarz Method for Variational Inequalities},
  author={Lori Badea and Xuecheng Tai and Junping Wang},
  journal={SIAM J. Numer. Anal.},
  year={2003},
  volume={41},
  pages={1052-1073}
}
This paper derives a linear convergence for the Schwarz overlapping domain decomposition method when applied to constrained minimization problems. The convergence analysis is based on a minimization approach to the corresponding functional over a convex set. A general framework of convergence is established for some multiplicative Schwarz algorithm. The abstract theory is particularly applied to some obstacle problems, which yields a linear convergence for the corresponding Schwarz overlapping… 
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70 Citations

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Pseudo-linear Convergence of an Additive Schwarz Method for Dual Total Variation Minimization

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Multilevel Schwarz method for the minimization with constraints of non-quadratic functionals.

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Global convergence rate of a standard multigrid method for variational inequalities

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  • 2014
A multigrid algorithm for variational inequalities whose constraints are of the two-obstacle type and the method is introduced as a subspace correction algorithm in a reflexive Banach space, proving its global convergence and estimating the error making some assumptions.

Schwarz methods for inequalities with contraction operators

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  • Mathematics, Computer Science
  • 2008

Convergence rate of some hybrid multigrid methods for variational inequalities

  • L. Badea
  • Mathematics, Computer Science
    J. Num. Math.
  • 2015
This algorithm together with other three algorithms, which are combinations of additive or multiplicative iterations on levels with additive or multiplier iterations over the levels, are analyzed in a unitary manner and in a more general framework which allow us to consider problems in the Sobolev space.

Multigrid methods for some quasi-variational inequalities

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  • Mathematics, Computer Science
  • 2013
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31 References

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The Schwarz domain decomposition method is proved to converge with a geometric rate depending on the decomposition of the domain based on an framework of convergence analysis established for general variational inequalities in Hilbert spaces.

Rate of Convergence for some constraint decomposition methods for nonlinear variational inequalities

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Abstract Convergence rate estimate is given for an overlapping domain decomposition method for obstacle problems. It is shown that the computed solution will converge monotonically to the true…

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In this paper, we prove a general approximation theorem useful in obtaining order of convergence estimates for the approximation of the solutions of a class of variational inequalities. The theorem…

Global and uniform convergence of subspace correction methods for some convex optimization problems

This paper gives some global and uniform convergence estimates for a class of subspace correction (based on space decomposition) iterative methods applied to some unconstrained convex optimization…

Convergence rate analysis of an asynchronous space decomposition method for convex Minimization

The convergence rate of an asynchronous space decomposition method for constrained convex minimization in a reflexive Banach space is analyzed, which generalizes the additive Schwarz domain decomposition methods to allow for asynchronous updates.

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In a Hilbert space an iterative process is defined which generalizes the Schwarz alternating method for nonlinear monotone problems to more than two subdomains and the convergence of this process is…

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