We present new algorithms for optimizing non-smooth, non-convex stochastic objectives
based on a novel analysis technique. This improves the current best-known complexity for …

We consider the optimization problem of the form $\min_ {x\in\mathbb {R}^ d} f
(x)\triangleq\mathbb {E}[F (x;\xi)] $, where the component $ F (x;\xi) $ is $ L $-mean-squared …

In this paper, we present several new results on minimizing a nonsmooth and nonconvex
function under a Lipschitz condition. Recent work shows that while the classical notion of …

Training neural networks requires optimizing a loss function that may be highly irregular,
and in particular neither convex nor smooth. Popular training algorithms are based on …

We study the impact of nonconvexity on the complexity of nonsmooth optimization,
emphasizing objectives such as piecewise linear functions, which may not be weakly …

We consider the oracle complexity of computing an approximate stationary point of a
Lipschitz function. When the function is smooth, it is well known that the simple deterministic …

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 …

We study the computational problem of the stationarity test for the empirical loss of neural
networks with ReLU activation functions. Our contributions are: Hardness: We show that …

Goldstein's 1977 idealized iteration for minimizing a Lipschitz objective fixes a distance-the
step size-and relies on a certain approximate subgradient. That" Goldstein subgradient" is …

Some Problems in Conic, Nonsmooth, and Online Optimization Page 1 Some Problems in
Conic, Nonsmooth, and Online Optimization Swati Padmanabhan A dissertation submitted in …