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 …

In this paper we consider finding a second-order stationary point (SOSP) of nonconvex
equality constrained optimization when a nearly feasible point is known. In particular, we first …

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 …

This paper proposes and analyzes a proximal augmented Lagrangian (NL-IAPIAL) method
for solving constrained nonconvex composite optimization problems, where the constraints …

In this paper, we consider minimization of a difference-of-convex (DC) function with and
without linear equality constraints. We first study a smooth approximation of a generic DC …

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

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 …

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 …