Author

Henry Wolkowicz

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Preprint Aug 2026

Optimal Nonergodic Primal-Dual Complexity of Efficient Inexact Parameter-Free Augmented Lagrangian Methods

Three inexact AL schemes are developed that preserve the standard AL subproblem structure and attain the optimal primal-dual complexity in the convex setting, improving prior AL bounds of $\mathcal O(\epsilon^{-4/3})$, $\mathcal O(\epsilon^{-7/4})$, and $\mathcal O(\epsilon^{-2})$, and removing the logarithmic factor from PAL guarantees.

Arnesh Sujanani, Saeed Ghadimi, Henry Wolkowicz · 0 citations