8 problems

Subtransversality conjecture. For alternating projections applied to inconsistent feasibility, subtransversality is necessary for R-linear convergence of the iterates to fixed poin…

Random-initialization convergence conjecture. When $m\geq Cn$, for $C>0$ large enough, alternating projections converge to the true solution with probability at least $1-\epsilon$.

Let Algorithm generate sequences $(x^k)_{k\in\mathds N}$ and $(z^k)_{k\in\mathds N}$ for the basis-pursuit problem. Convergence conjecture. Algorithm always converges to a solution…

Projection-sign conjecture. For any $w\in C_2$, either

Let $A$ and $B$ be the two sets involved in a nonconvex alternating projections algorithm, and let subtransversality denote the regularity property imposed explicitly or implicitly…

Deutsch and Hundal's conjecture. If $(\lambda_n)$ tends to $0$ sufficiently slowly, then

Let $X$ be a Hilbert space, let $M1, dots,MN$ be closed subspaces, and write … Assume that $M_1^\perp+\cdots+M_N^\perp$ is not closed, so that the subspaces are aligned, and let…

Let $M$ and $N$ be algebraic manifolds, and consider the sequence obtained by alternating projections between them. Convergence conjecture. For algebraic manifolds, the sequence of…