8 problems

Let Two-Sided L-BFGS denote the proposed limited-memory BFGS algorithm using the $[\epsilon,M]$ geometric envelope safeguard, and let standard L-BFGS denote the corresponding metho…

qNBO initialization conjecture. In practice, a few initial gradient descent steps are sufficient, although they are necessary for the theoretical analysis.

Classical quasi-Newton steps conjecture. We conjecture that IQN and SLIQN contain the steps of classical quasi-Newton updates.

In decentralized stochastic optimization, let gradient and Hessian estimators be constructed using mini-batches in the proposed variance-reduced stochastic second-order methods. La…

Let SR1 and BFGS denote the symmetric rank-one and Broyden–Fletcher–Goldfarb–Shanno quasi-Newton methods, respectively. Rodomanov's conjecture. SR1 and BFGS methods might have fast…

The limited-memory BFGS method with displacement aggregation, denoted texttt{Agg-BFGS}, is applied repeatedly to curvature information over a sequence of iterations. The resulting…

BFGS for the unit ball. The trial step $s$ converges to zero.

Let ${\bf A}$ be an invertible matrix and consider stochastic quasi-Newton rules obtained by applying the paper's stochastic reformulation and its basic, parallel, or accelerated s…