Composite optimization offers a powerful modeling tool for a variety of applications and is
often numerically solved by means of proximal gradient methods. In this paper, we consider …

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 …

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 the problem of minimizing a non-convex function over a smooth manifold M.
We propose a novel algorithm, the Orthogonal Directions Constrained Gradient Method …

In this paper we study a class of nonconvex optimization which involves uncertainty in the
objective and a large number of nonconvex functional constraints. Challenges often arise …

Many real-world problems not only have complicated nonconvex functional constraints but
also use a large number of data points. This motivates the design of efficient stochastic …

The primary goal of this paper is to provide an efficient solution algorithm based on the
augmented Lagrangian framework for optimization problems with a stochastic objective …

This paper establishes the iteration complexity of an inner accelerated inexact proximal
augmented Lagrangian (IAIPAL) method for solving linearly constrained smooth nonconvex …

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