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A new descent alternating direction method with LQP regularization for the structured variational inequalities

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Abstract

In this paper, we suggest and analyze a new logarithmic–quadratic proximal alternating direction scheme for the separable constrained convex programming problem. The main contribution of this paper, the predictor is obtained via solving LQP system approximately under significantly relaxed accuracy criterion and the new iterate is obtained by using a new direction with a new step size \(\alpha _k\). Global convergence of the proposed method is proved under certain assumptions. We also reported some numerical results to illustrate the efficiency of the proposed method.

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Acknowledgements

The first author is grateful to Prof. Hafida Bouloiz for her constant help.

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Authors and Affiliations

  1. School of Management and Engineering, Nanjing University, Nanjing, 210093, People’s Republic of China

    Abdellah Bnouhachem

  2. ENSA, Ibn Zohr University, BP 1136, Agadir, Morocco

    Abdellah Bnouhachem

  3. Department of Mathematics, National Technical University of Athens, Zografou Campus, 157 80, Athens, Greece

    Themistocles M. Rassias

Authors
  1. Abdellah Bnouhachem
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  2. Themistocles M. Rassias
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Correspondence to Abdellah Bnouhachem.

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Bnouhachem, A., Rassias, T.M. A new descent alternating direction method with LQP regularization for the structured variational inequalities. Optim Lett 13, 175–192 (2019). https://doi.org/10.1007/s11590-018-1262-x

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