13 problems

Let $g$ be a $mu_g$-strongly convex and $L_g$-smooth function, and let $M$ belong to the class of linear operators with singular values in $[mu_M,L_M]$. Write…

Let $\mathcal{F}_{L,D}$ be the class of pairs $(f,x_0)$ where $f$ is $L$-smooth and convex, has a minimizer $x_\star$ with $\|x_0-x_\star\|\leq D$, and $x_N$ is obtained by $N$ ste…

Let $f\colon\mathbb{R}^n\rightarrow\mathbb{R}$ be an $L$-smooth convex function. For an initialization $x_0$ and $N$ steps of gradient descent with constant stepsize…

Let $\mu\in(-\infty,0)$ and consider $N$ iterations of gradient descent with constant stepsize $\gamma L\in[\gbari[\bar{N}-1],\gbari[\bar{N}])\subseteq[\gbari[1],\gbari[N-1])$, sta…

Let $f\in\mathcal{F}_{\mu,L}$ with $\mu\in(-\infty,0)$, and consider $N$ gradient-descent iterations from $x_0$ with stepsizes satisfying $\gamma_iL\in[1,\gbari[1]]$ for…

Let $f$ belong to the function class considered in the paper, let $abla f(xi)$ denote the gradient along the gradient-descent iterates, and let the stepsizes $gammai$ be chosen as…

Consider gradient descent run for a fixed number $N$ of steps with constant stepsize $h\in(0,1]$, starting from $x_0$ with $\lVert x_0-x_\star\rVert=D$. For simple extrapolation by…

OGM-G lower-bound conjecture. The lower bound above for OGM-G under the distance initialization condition is exact. This is posed as an open problem and is supported by numerical e…

Let OGM-G be the first-order method discussed in the source, with worst-case gradient bound given by equation. OGM-G optimality conjecture. The exact worst-case bound of OGM-G may…

Taylor et al.'s one-step gradient-decrease conjecture. The optimal step size in terms of gradient decrease is $h=\sqrt{2}$, with worst-case bound

FGM and OGM secondary-iterate conjecture. The final secondary iterate satisfies

Strongly convex gradient-norm conjecture. Every sequence of iterates generated in this way satisfies

Drori–Teboulle conjecture. Every sequence of iterates generated in this way satisfies