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Res."],"published-print":{"date-parts":[[2026,2]]},"abstract":"<jats:p>We propose an inexact linearized augmented Lagrangian method for the linear equality constrained convex programming, for which the objective function has a \u201cnonsmooth + smooth\u201d composite structure. We show that both the objective error and the constraint gap associated with the proposed algorithm enjoy an [Formula: see text] nonergodic convergence rate. By choosing a specific proximal matrix, we drive a customized linearized augmented Lagrangian method for the problem, where the subproblem can be solved by means of the proximal mapping of a convex function. 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