Adaptive inexact fast augmented Lagrangian methods for constrained convex optimization

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In this paper we analyze several inexact fast augmented Lagrangian methods for solving linearly constrained convex optimization problems. Mainly, our methods rely on the combination of excessive-gap-like smoothing technique developed in [15] and the newly introduced inexact oracle framework from [4]. We analyze several algorithmic instances with constant and adaptive smoothing parameters and derive total computational complexity results in terms of projections onto a simple primal set. For the basic inexact fast augmented Lagrangian algorithm we obtain the overall computational complexity of order O(1ε⁵/⁴), while for the adaptive variant we get O(1ε), projections onto a primal set in order to obtain an ε-optimal solution for our original problem.