An accelerated inexact dampened augmented Lagrangian method for linearly-constrained nonconvex composite optimization problems

This paper proposes and analyzes an accelerated inexact dampened augmented Lagrangian (AIDAL) method for solving linearly-constrained nonconvex composite optimization problems. Each iteration of the AIDAL consists of: (i) inexactly a proximal (AL) subproblem by calling gradient (ACG) subroutine; (ii) applying under-relaxed Lagrange multiplier update; (iii) using novel test to check whether penalty parameter AL function should be increased. Under several mild assumptions involving dampening factor under-relaxation constant, it is shown that generates approximate stationary point constrained problem in $$\mathcal{O}(\varepsilon ^{-5/2}\log \varepsilon ^{-1})$$ iterations ACG subroutine, given tolerance $$\varepsilon >0$$ . Numerical experiments are also show computational efficiency proposed method.