Nonconvex-concave min-max problem arises in many machine learning applications
including minimizing a pointwise maximum of a set of nonconvex functions and robust …

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 …

This work develops analysis and algorithms for solving a class of bilevel optimization
problems where the lower-level (LL) problems have linear constraints. Most of the existing …

First-order methods have been studied for nonlinear constrained optimization within the
framework of the augmented Lagrangian method (ALM) or penalty method. We propose an …

Bilevel optimization is one of the fundamental problems in machine learning and
optimization. Recent theoretical developments in bilevel optimization focus on finding the …

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 objective while preserving the privacy
of the examples in the training data. Building upon the previous variance-reduced algorithm …

The standard simplex in, also known as the probability simplex, is the set of nonnegative
vectors whose entries sum up to 1. It frequently appears as a constraint in optimization …

Nonconvex constrained optimization problems can be used to model a number of machine
learning problems, such as multi-class Neyman-Pearson classification and constrained …

We study the smooth minimax optimization problem $\min_ {\bf x}\max_ {\bf y} f ({\bf x},{\bf y})
$, where $ f $ is $\ell $-smooth, strongly-concave in ${\bf y} $ but possibly nonconvex in ${\bf …