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On the convergence of a Jacobi-type algorithm for Singly Linearly-Constrained Problems Subject to simple Bounds

Author

Listed:
  • Giampaolo Liuzzi

    (Consiglio Nazionale delle Ricerche - Istituto di Analisi dei Sistemi ed Informatica "A. Ruberti" (CNR - IASI) - Viale Manzoni 30 - Rome, Italy. Tel.: +39-06-7716439, Fax: +39-06-7716461)

  • Laura Palagi

    (Sapienza Universita' di Roma - Dipartimento di Informatica e Sistemistica, Rome, Italy)

  • Mauro Piacentini

    (Sapienza Universita' di Roma - Dipartimento di Informatica e Sistemistica A. Ruberti (DIS) - Via Ariosto 25 - Rome, Italy. Tel.: +39-06-77274085)

Abstract

In this work we define a block decomposition Jacobi-type method for nonlinear optimization problems with one linear constraint and bound constraints on the variables. We prove convergence of the method to stationary points of the problem under quite general assumptions.

Suggested Citation

  • Giampaolo Liuzzi & Laura Palagi & Mauro Piacentini, 2010. "On the convergence of a Jacobi-type algorithm for Singly Linearly-Constrained Problems Subject to simple Bounds," DIS Technical Reports 2010-01, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    • Handle: RePEc:aeg:wpaper:2010-1
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    File URL: http://www.dis.uniroma1.it/~bibdis/RePEc/aeg/wpaper/2010-01.pdf
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    References listed on IDEAS

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    1. C. J. Lin & S. Lucidi & L. Palagi & A. Risi & M. Sciandrone, 2009. "Decomposition Algorithm Model for Singly Linearly-Constrained Problems Subject to Lower and Upper Bounds," Journal of Optimization Theory and Applications, Springer, vol. 141(1), pages 107-126, April.
    2. Joachims, Thorsten, 1998. "Making large-scale SVM learning practical," Technical Reports 1998,28, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
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    Cited by:

    1. Andrea Manno & Laura Palagi & Simone Sagratella, 2014. "A Class of Convergent Parallel Algorithms for SVMs Training," DIAG Technical Reports 2014-17, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    2. Andrea Manno & Laura Palagi & Simone Sagratella, 2018. "Parallel decomposition methods for linearly constrained problems subject to simple bound with application to the SVMs training," Computational Optimization and Applications, Springer, vol. 71(1), pages 115-145, September.
    3. Amir Beck, 2014. "The 2-Coordinate Descent Method for Solving Double-Sided Simplex Constrained Minimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 162(3), pages 892-919, September.
    4. Andrea Cristofari, 2019. "An almost cyclic 2-coordinate descent method for singly linearly constrained problems," Computational Optimization and Applications, Springer, vol. 73(2), pages 411-452, June.

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