11 problems

Convergence conjecture. For $\kappa\to+\infty$, this randomized cyclic coordinate-ascent algorithm cannot get stuck at a suboptimal point and therefore converges to a maximum of th…

General iterative quantization conjecture. The main task in designing iterative message-passing algorithms for more general quantization problems lies in designing appropriate tie-…

R2N2 approximation conjecture. A recursively recurrent neural network (R2N2) can approximate many traditional numerical algorithms based on Taylor series expansions.

Conjecture. By reordering the indices if necessary, there exists an $N_0$ such that the following inequalities hold. The supplied statement span does not include the inequalities t…

Let $K$ be the monotone cone used in the cone projected power iteration, and let the iterated vector be updated by projecting onto $K$. Monotone-cone convergence conjecture. The mo…

Hollowed-Lloyd optimality conjecture. The conditions

Let $m$ and $n$ be the parameters of the Arimoto algorithm, and suppose that the equivalence … holds for $m=3$ under the stated assumptions. Arimoto convergence equivalence. The sa…

Consider the basis pursuit problem … where $x\in\mathbb R^n$, $A\in\mathbb R^{m\times n}$, and $b\in\mathbb R^m$. Starting from $y^{(0)}\in\mathbb R^n$, generate the IRLS sequence…

ITKM basin-of-attraction conjecture. The basin of attraction is conjectured to have size

Let the vertices be points in Euclidean space, and suppose that the convex hull of the set of vertices is of full dimension. Starting from an initial point, apply the Weiszfeld alg…

A linear system with a triangular-shaped matrix is considered in the expectation propagation algorithm setting described above. Finite-step convergence conjecture. The convergence…