34 problems

John–Mitchell conjecture. If an incomplete block design is $D$-optimal, $A$-optimal, or $E$-optimal, then it is an RGD, provided that an RGD exists.

Let minimizing sequences for the compliance-location problem be configurations of balls whose centres are placed in a domain, with $d$ denoting the spatial dimension. In dimension…

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 $\{p_n\}_{n=1}^\infty$ be a decreasing sequence with $1<p_n<\infty$ and $p_n\to1$. For each $n$, let $(\hat{k}_n,\hat{\mu}_n)$, $\hat{\boldsymbol{\tau}}_n$, and…

Persistence conjecture. If ${\bm{w}}^*_k=0$, then ${\bm{w}}^{*p}_k=0$ for $p<1$ as well.

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…

Let $c$ parameterize the design correlation, and let the known-sign and unknown-sign summary criteria be denoted by $\psi_\Lambda(c)$, $\psi_{\max}(c)$, $\psi_\Lambda^{\pm}(c)$, an…

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

Extension property conjecture. Any such monotone map ${\mathbf{v}}_0$ has the extension property.

Nonexistence and A-optimality conjecture. The hypothetical plan ${\cal P}^*$ does not exist, and ${\cal P}_2$ is A-optimal.

Let an excitation and measurement placement (EMP) be an allocation of excitations and measurements in a dynamic network, and let the covariance matrix refer to the theoretical cova…

One-point quantitative-design conjecture. The determinant $\det(\mathbf{M}(\bar{\xi}_{1;\mathbf{d}}\otimes\xi_2))$ will be maximized by a marginal one-point design

Balanced-orbit conjecture. The result that the optimal orbit balances, as far as possible, the numbers of attributes in which any two alternatives differ will be valid for any numb…

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 $K$ be one of the scalar fields under consideration, and let an optimal measure be a measure maximizing the relevant $q$-th moment among isotropic measures. A support is non-di…

Conjecture on simultaneous A- and D-optimality. Among RGDs, the same design is $A$-optimal and $D$-optimal.

Consider the Bradley–Terry model with $5$ alternatives, pairwise-comparison intensities $\lambda_{ij}$, and a full support $D$-optimal design with weight $w_{ij}$ on pair $(i,j)$.…

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 $\beta>0$ and $0<\delta<\dfrac{\beta|\Omega|}{\beta+1}$. For a measurable set $D\subset\Omega$ with $|D|=\delta$, define … and let … Here $D^*$ denotes a minimizer of this opti…

Consider the Fourier regression and its mathematically equivalent weighted polynomial regression, together with the Möbius group acting on the designs. A design is D-optimal when i…

Let $n$ denote the number of terms in the Fourier regression, and consider the discrete uniform design with equally spaced design points and equal weights. The corresponding weight…

Let $d=1$ and $k=4$, so that $p=5$ and a saturated design is specified by a support $X\subset\{0,1\}^4$ with $|X|=5$. After quotienting by the hyperoctahedral symmetry, there are 1…