Comparing, or benchmarking, of optimization algorithms is a complicated task that involves
many subtle considerations to yield a fair and unbiased evaluation. In this paper, we …

In this paper, we introduce a stochastic projected subgradient method for weakly convex (ie,
uniformly prox-regular) nonsmooth, nonconvex functions---a wide class of functions which …

We present a framework for analyzing convergence and local rates of convergence of a
class of descent algorithms, assuming the objective function is weakly convex. The …

We study convergence rates of the classic proximal bundle method for a variety of
nonsmooth convex optimization problems. We show that, without any modification, this …

For a class of nonconvex nonsmooth functions, we consider the problem of computing an
approximate critical point, in the case when only inexact information about the function and …

We consider the problem of minimizing the difference of two nonsmooth convex functions
over a simple convex set. To deal with this class of nonsmooth and nonconvex optimization …

Algorithms for problem decomposition and splitting in optimization and the solving of
variational inequalities have largely depended on assumptions of convexity or monotonicity …

An optimization algorithm for nonsmooth nonconvex constrained optimization problems with
upper-objective functions is proposed and analyzed. Upper-is a weakly concave property …

Constrained optimization problems where both the objective and constraints may be
nonsmooth and nonconvex arise across many learning and data science settings. In this …

We consider the long-term dynamics of the vanishing stepsize subgradient method in the
case when the objective function is neither smooth nor convex. We assume that this function …