This monograph covers some recent advances in a range of acceleration techniques
frequently used in convex optimization. We first use quadratic optimization problems to …

In this paper, we study the fundamental open question of finding the optimal high-order
algorithm for solving smooth convex minimization problems. Arjevani et al.(2019) …

We consider the problem of minimizing a continuous function given given access to a
natural quantum generalization of a stochastic gradient oracle. We provide two new …

We develop a variant of the Monteiro-Svaiter (MS) acceleration framework that removes the
need to solve an expensive implicit equation at every iteration. Consequently, for any $ p\ge …

In this merged paper, we consider the problem of minimizing a convex function with
Lipschitz-continuous $ p $-th order derivatives. Given an oracle which when queried at a …

Do you know the difference between an optimist and a pessimist? The former believes we
live in the best possible world, and the latter is afraid that the former might be right.… In that …

We propose a near-optimal method for highly smooth convex optimization. More precisely,
in the oracle model where one obtains the $ p^{th} $ order Taylor expansion of a function at …

In this paper, we provide near-optimal accelerated first-order methods for minimizing a
broad class of smooth nonconvex functions that are unimodal on all lines through a …

Although Nesterov's accelerated gradient method (AGM) has been studied from various
perspectives, it remains unclear why the most popular forms of AGMs must handle convex …

In this paper, we propose an accelerated quasi-Newton proximal extragradient method for
solving unconstrained smooth convex optimization problems. With access only to the …