10 problems

Let the data points lie in a symmetrically perpendicular CAT($\kappa$) space, and consider an iteration formed from compositions and convex combinations of proximal mappings of the…

Let a CAT($\kappa$) space have sufficiently small diameter that it is symmetric perpendicular, and let a fixed-point mapping be a self-mapping formed from compositions and convex c…

Let the underlying space be a Hadamard space, let the data points be points in that space, and consider an iteration formed from compositions and convex combinations of proximal ma…

Let $A\in\mathbb{R}^{m\times n}$ have rank $m$, let $({\bm u}^*,{\bm v}^*)$ be a global minimizer of $g({\bm u},{\bm v})$ with ${\bm z}^*={\bm u}^*\circ{\bm v}^*$, and let…

Let $f$ and $g$ belong to the function classes $\mathcal{F}_{\rho,\alpha^{-1}}$ and $\mathcal{F}_{\mu,\beta^{-1}}$, respectively, and consider the optimization problem … Here GM, F…

Let Algorithm generate a sequence $\{y^k\}$, and suppose that its Step is equivalently implemented using in place of. Complexity conjecture. The complexity estimate of Algorithm sh…

The sparse variant is an algorithmic variant of the variance-reduced three-operator splitting method discussed above; its iterates have a convergence rate measured as a function of…

Sharp subcritical convergence-rate conjecture. Given the results obtained in the continuous case, one should have

Convergence conjecture. The proposed algorithm can be used without concern about non-convergence; in particular, the sequence of iterates $\vec{x}^{(k,I+1)}$ is expected to converg…

Restart conjecture. Restarting could improve the performance of FISTA even in the presence of nonsmooth regularizers.