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Convex constrained optimization for large-scale generalized Sylvester equations

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Abstract

We propose and study the use of convex constrained optimization techniques for solving large-scale Generalized Sylvester Equations (GSE). For that, we adapt recently developed globalized variants of the projected gradient method to a convex constrained least-squares approach for solving GSE. We demonstrate the effectiveness of our approach on two different applications. First, we apply it to solve the GSE that appears after applying left and right preconditioning schemes to the linear problems associated with the discretization of some partial differential equations. Second, we apply the new approach, combined with a Tikhonov regularization term, to restore some blurred and highly noisy images.

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Authors and Affiliations

  1. L.M.P.A., Université du Littoral, 50 rue F. Buisson BP699, 62228, Calais-Cedex, France

    A. Bouhamidi & K. Jbilou

  2. Departamento de Cómputo Científico y Estadística, Universidad Simón Bolívar (USB), Ap. 89000, Caracas, 1080-A, Venezuela

    M. Raydan

Authors
  1. A. Bouhamidi
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  2. K. Jbilou
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  3. M. Raydan
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Correspondence to M. Raydan.

Additional information

The research of M. Raydan was partially supported by USB and the Scientific Computing Center at UCV.

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Bouhamidi, A., Jbilou, K. & Raydan, M. Convex constrained optimization for large-scale generalized Sylvester equations. Comput Optim Appl 48, 233–253 (2011). https://doi.org/10.1007/s10589-009-9253-6

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