6 problems

Let $N$ denote the iteration count and let the performance criterion be the minimum squared gradient norm, $\min_{k\in\{1,\ldots,N\}}\|\nabla f(x_k)\|^2$, for minimizing a smooth c…

Let $N$ denote the iteration count, and consider full fixed-step cyclic coordinate descent on a problem partitioned into $2$ blocks, allowing the update to use all past gradient in…

Let $\mathcal{J}$ be a finite index set, and for each $j\in\mathcal{J}$ let $f_j$ be a convex $(M_j,v_j)$-Hölder smooth function. Let $x_0$ be the initial point, $x^*$ an optimizer…

OBL-G$_\flat$'s $\mathcal{A}^\star$-optimality conjecture. OBL-G$_\flat$ is $\mathcal{A}^\star$-optimal in the sense that

Let a first-order algorithm have $T$ steps of memory. For each integer $n\geq 1$, an off-by-$n$ pointwise IQC is the quadratic constraint associated with a pair of iterates…

Let $x_0,x_1,\dots$ and $y_1,y_2,\dots$ be the main and auxiliary sequences, respectively, defined by the fast gradient method (FGM), and let $f$ be the objective function in the c…