## Complexity of a quadratic penalty accelerated inexact proximal point method for solving linearly constrained nonconvex composite programs. (arXiv:1802.03504v1 [math.OC])

This paper analyzes the iteration-complexity of a quadratic penalty
accelerated inexact proximal point method for solving linearly constrained
nonconvex composite programs. More specifically, the objective function is of
the form $f + h$ where $f$ is a differentiable function whose gradient is
Lipschitz continuous and $h$ is a closed convex function with bounded domain.
The method, basically, consists of applying an accelerated inexact proximal
point method for solving approximately a sequence of quadratic penalized
subproblems associated to the linearly constrained problem. Each subproblem of
the proximal point method is in turn approximately solved by an accelerated
composite gradient method. It is shown that the proposed scheme generates a
$\rho$-approximate stationary point in at most ${\cal{O}}(1/\rho^{3})$.
Finally, numerical results showing the efficiency of the proposed method are
also given.查看全文