Functional constrained optimization is becoming more and more important in machine
learning and operations research. Such problems have potential applications in risk-averse …

Consider the minimization of a nonconvex differentiable function over a bounded
polyhedron. A popular primal-dual first-order method for this problem is to perform a gradient …

This paper presents smoothing schemes for obtaining approximate stationary points of
unconstrained or linearly constrained composite nonconvex-concave min-max (and hence …

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 …

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 …

Error bound analysis, which estimates the distance of a point to the solution set of an
optimization problem4 using the optimality residual, is a powerful tool for the analysis of first …

Minimax optimization has served as the backbone of many machine learning problems.
Although the convergence behavior of optimization algorithms has been extensively studied …

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 …

With the rapid development of battery electric buses (BEBs) in urban public traffic, it arises
the problem of BEB charging scheduling, which aims to supply electric power for all the …

In this paper, we present new stochastic methods for solving two important classes of
nonconvex optimization problems. We first introduce a randomized accelerated proximal …