This paper establishes the iteration complexity of an inner accelerated inexact prox-imal augmented Lagrangian (IAIPAL) method for solving linearlyconstrainedsmoothnonconvexcomposite optimization problems that is ...
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This paper establishes the iteration complexity of an inner accelerated inexact prox-imal augmented Lagrangian (IAIPAL) method for solving linearlyconstrainedsmoothnonconvexcomposite optimization problems that is based on the classical augmented Lagrangian (AL) func-tion. More specifically, each IAIPAL iteration consists of inexactly solving a proximal AL subprob-lem by an accelerated composite gradient (ACG) method followed by a classical Lagrange multiplier update. Under the assumption that the domain of the composite function is bounded and the prob-lem has a Slater point, it is shown that IAIPAL generates an approximate stationary solution in O(\varepsilon -5/2 log2\varepsilon -1) ACG iterations where \varepsilon > 0 is a tolerance for both stationarity and feasibility. Moreover, the above bound is derived without assuming that the initial point is feasible. Finally, numerical results are presented to demonstrate the strong practical performance of IAIPAL.
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