Efficient Convex Optimization Requires Superlinear Memory

Annie Marsden, Vatsal Sharan, Aaron Sidford, Gregory Valiant

Abstract: We show that any memory-constrained, first-order algorithm which minimizes $d$-dimensional, $1$-Lipschitz convex functions over the unit ball to $1/\mathrm{poly}(d)$ accuracy using at most $d^{1.25...