11 problems

Let $R_m$ and $S_m$ denote the corresponding error bounds for parameters $ell\hspace{0.25ex}\in[\frac12,1]$, $\alpha\in[\frac12,1]$, and integer $m\geq 1$. The relative error is…

Let $\pmb{\mu}_{\mathrm{pr}}$ be the prior mean and let $\mathbf{L}_{\mathrm{pr}}$ be a prior covariance factor appearing in the finite-dimensional linear Gaussian inverse problem,…

Let $\bm{w}$ and $\bm{w}_*$ denote points in the algorithm's variable space, let $F$ be the residual mapping, and let $\operatorname{dist}(\bm{w},\bm{w}_*)$ denote the distance bet…

Dimensional-dependence conjecture. The dependence on $d_x$ present in the authors' results but absent from the results of Akyildiz is solely due to their bounds controlling the err…

Let ${\cal M}$ be a complete Riemannian manifold with dimension $n\geq 2$, and let $p\in\Omega$ be a feasible point at which CRSC or RCPLD is satisfied. Here, $\Omega$ denotes the…

Let $f$ and $g$ be the functions defining the global error-bound stability notions in parts (ii) and (iii) of Theorem 3.3, and let condition (3-9) be the condition discussed there.…

Conjecture. A similar quadratic growth result on every sublevel set of the dual problem should hold when Slater's condition is replaced by the linear regularity condition $$ .

For $p$-cones, let … where $\|\cdot\|_{p}$ denotes the $p$-norm, and let $\epsilon$ and $\kappa$ denote the quantities in the facial residual function construction. Facial residual…

Logarithmic-factor improvement conjecture. For any $a$ and $\alpha$, this logarithmic factor can generally be improved so that it is bounded by a numerical constant whenever…

Let $a_1,a_2,\ldots,a_n$ be floating-point numbers, let $\pi_n=a_1a_2\cdots a_n$ be their exact product, and let $\widehat{\pi}_n$ be the value computed by successive rounded multi…

Sharp error-bound conjecture. The displayed quantity upper bounds the estimation error \|\hat\mathbf{x}-\mathbf{x}_0\| for arbitrary values of the noise variance $\sigma^2$.