Abstract
In this work, Solodov–Svaiter's hybrid projection-proximal and extragradient-proximal methods [16,17] are used to derive two algorithms to find a Karush–Kuhn–Tucker pair of a convex programming problem. These algorithms are variations of the proximal augmented Lagrangian. As a main feature, both algorithms allow for a fixed relative accuracy of the solution of the unconstrained subproblems. We also show that the convergence is Q-linear under strong second order assumptions. Preliminary computational experiments are also presented.
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Humes, C., Silva, P.J. & Svaiter, B.F. Some Inexact Hybrid Proximal Augmented Lagrangian Algorithms. Numerical Algorithms 35, 175–184 (2004). https://doi.org/10.1023/B:NUMA.0000021768.30330.4b
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DOI: https://doi.org/10.1023/B:NUMA.0000021768.30330.4b