7 problems

Let $U$ and $V$ be subspaces and let $P_U$ and $P_V$ denote the corresponding orthogonal projections. Consider the composition … where $R_U$ and $R_V$ are the associated reflected…

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

Let $K$ and $U$ be the sets in the preceding convergence setting, with $U$ intersecting the interior of $K$. The circumcentered-reflection method (CRM) generates an iterative seque…

De Pierro's conjecture. The least-squares solution set $S$ is nonempty if and only if, for every starting point $u_0$, the limits

Let $K$ be a Hilbert lattice cone and let $A$ be a finite-codimension closed affine manifold. For parameters $0\leq a,b,c<1$, consider the relaxed Douglas–Rachford iteration define…

De Pierro's conjecture. As $\varepsilon\to0$, these limit cycles shrink towards a single point which is a minimizer of $\Phi$, equivalently a fixed point of the composition operato…

Let $M_\epsilon$ be the parameterized sets considered in the local convergence result, and suppose the assumptions that these sets are prox-regular and have nontrivial proximal nor…