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\(O(1/k^2)\) convergence rates of (dual-primal) balanced augmented Lagrangian methods for linearly constrained convex programming

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Abstract

The recent balanced augmented Lagrangian method (ALM) and its dual-primal version are effective for solving linearly constrained convex programming problems. We present accelerated (dual-primal) balanced ALM methods and establish \(\varvec{O(1/k^2)}\) (where \(\varvec{k}\) is the number of iterations) convergence rates in the case that the objective function to be minimized is strongly convex. Numerical results demonstrate the efficiency of the new accelerated algorithms.

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Acknowledgements

The authors would like to express their very great appreciation to the editor and all reviewers.

Funding

This research was supported by the National Natural Science Foundation of China under grant 12171021, and the Fundamental Research Funds for the Central Universities.

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Authors and Affiliations

  1. School of Mathematical Sciences, Beihang University, Beijing, 100191, People’s Republic of China

    Tao Zhang, Yong Xia & Shiru Li

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  1. Tao Zhang
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  2. Yong Xia
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  3. Shiru Li
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All authors reviewed the manuscript. All authors contributed equally to this work.

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Correspondence to Shiru Li.

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Zhang, T., Xia, Y. & Li, S. \(O(1/k^2)\) convergence rates of (dual-primal) balanced augmented Lagrangian methods for linearly constrained convex programming. Numer Algor (2024). https://doi.org/10.1007/s11075-024-01796-x

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