2 research outputs found
Iteration-complexity of an inner accelerated inexact proximal augmented Lagrangian method based on the classical Lagrangian function and a full Lagrange multiplier update
This paper establishes the iteration-complexity of an inner accelerated
inexact proximal augmented Lagrangian (IAIPAL) method for solving
linearly-constrained smooth nonconvex composite optimization problems that is
based on the classical augmented Lagrangian (AL) function. More specifically,
each IAIPAL iteration consists of inexactly solving a proximal AL subproblem 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 problem has a Slater point, it is shown that IAIPAL
generates an approximate stationary solution in ACG
iterations (up to a logarithmic term) where is the 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