In this paper, an inexact proximal-point penalty method is studied for constrained
optimization problems, where the objective function is non-convex, and the constraint …

We analyze the sample complexity of single-loop quadratic penalty and augmented
Lagrangian algorithms for solving nonconvex optimization problems with functional equality …

Strong variational sufficiency is a newly proposed property, which turns out to be of great
use in the convergence analysis of multiplier methods. However, what this property implies …

We consider a non-convex constrained optimization problem, where the objective function is
weakly convex and the constraint function is either convex or weakly convex. To solve this …

It is well-known that the lower bound of iteration complexity for solving nonconvex
unconstrained optimization problems is $\Omega (1/\epsilon^ 2) $, which can be achieved …

This work presents an adaptive superfast proximal augmented Lagrangian (AS-PAL)
method for solving linearly-constrained smooth nonconvex composite optimization …

In this paper, we propose a unified primal-dual algorithm framework based on the
augmented Lagrangian function for composite convex problems with conic inequality …

This paper proposes and establishes the iteration complexity of an inexact proximal
accelerated augmented Lagrangian (IPAAL) method for solving linearly constrained smooth …

Classical primal-dual algorithms attempt to solve by alternately minimizing over the primal
variable through primal descent and maximizing the dual variable through dual ascent …

Classical primal-dual algorithms attempt to solve $\max_ {\mu}\min_ {x}\mathcal {L}(x,\mu) $
by alternatively minimizing over the primal variable $ x $ through primal descent and …