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We present new algorithms for stochastic optimization problems in which the objective is neither smooth nor convex, subject to a convex constraint set. Our algorithms return a $(\delta,\varepsilon)$-Goldstein stationary point, as recently defined for constrained problems by Liu et al. (2024), with improved complexities...
We study the complexity of finding $(\delta,\epsilon)$-Goldstein stationary points of nonsmooth nonconvex Lipschitz functions. By now, it is known that randomized first-order algorithms can solve this task with a dimension-free oracle complexity [Zhang et al., 2020], whereas deterministic algorithms cannot, as their co...
A tight lower bound is proved of $\Omega(\lambda^{1/2}\epsilon^{-7/2})$ for finding points satisfying the recently proposed relaxed notion of $(\lambda,\epsilon)$-stationarity, which allows combining further-away gradients.
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