9 problems

Hendrych's NP-hardness conjecture. The Bayesian AOD problem is NP-hard. This conjecture is resolved in the source: the paper proves NP-hardness for its regularized A-optimal design…

Let $p\in(1,\infty)$ and $t_{\max}>0$. For each natural number $n$, let $(\hat{k}_n,\hat{\mu}_n)\in L^\infty(\Omega;\mathbb{R}_+)^2$ solve the (vp-IMD) problem, respectively the (s…

Let $q>0$ be the charge parameter, and consider the minimization problem defined by equation (minmin1), whose minimizers are configurations attaining its minimum energy. Nonexisten…

Gamma-bound dominance conjecture. For $s-q\geq 1$, we have

Let $\Omega$ be a bounded convex domain, and let the load $f \in \mathcal{M}(\overline{\Omega};\mathbb{R})$ be finitely supported. An optimal string system consists of a pair…

Decomposability conjecture. The graph $G$ of a $D$-optimal design in the Bradley--Terry model is decomposable.

Let $K$ be the dimension, let $D$ be the covariance matrix of the random coefficients, and let $(d_0,d_1,d_2)^T\in\mathcal{C}_K$ denote its parameter vector. A rhombic design is an…

Let $m$ be the number of alternatives, let $\binom{m}{2}$ pairwise-comparison intensities be denoted by $\boldsymbol{\lambda}=(\lambda_{ij})$, and let $w_{ij}$ be the weights of a…

Let $r$ denote the number of runs, and distinguish affinely full-dimensional factorial designs from subset fractional factorial designs. The D-optimal design conjecture. The $D$-op…