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A self-adaptive descent LQP alternating direction method for the structured variational inequalities

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Abstract

In this paper, by combining the logarithmic-quadratic proximal (LQP) method and alternating direction method, we proposed an LQP alternating direction method for solving structured variational inequalities. The new iterate is generated by searching the optimal step size along a descent direction with a new step size αk. The choice of the descent direction and the step size selection strategies are important for the algorithm’s efficiency. The O(1/t) convergence rate of the proposed method is studied, and its efficiency is also verified by some numerical experiments.

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Authors and Affiliations

  1. Equipe MAISI, Ibn Zohr University, ENSA, BP 1136, Agadir, Morocco

    Abdellah Bnouhachem

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  1. Abdellah Bnouhachem
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Correspondence to Abdellah Bnouhachem.

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This paper is dedicated to Mohamed Bnouhachem and Mohamed Khalfaoui

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Bnouhachem, A. A self-adaptive descent LQP alternating direction method for the structured variational inequalities. Numer Algor 86, 303–324 (2021). https://doi.org/10.1007/s11075-020-00890-0

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  • DOI: https://doi.org/10.1007/s11075-020-00890-0

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