Near-Optimal Acceleration for Smooth $\ell_p$ / $\ell_q$ Nondual Convex First-Order Oracle Optimization

Abstract

We study the optimization of convex objectives with $(L,\kappa-1)$-H\"older-continuous gradients in $\ell_q$ over $R B_p^d$, $1<\kappa\le 2$. (MG26) provides selectors with a movement bound for the problem of chasing high-dimensional convex nested sets for every $p