8 problems

Unconditional convergence conjecture. The algorithm $$ converges unconditionally for $(\alpha,\beta,\theta)\in\mathbb{R}^2_{++}\times(\mathbb{R}\setminus\{0\})$ over $\mathcal{A}\t…

Equality conjecture. If $M$ is a CMQd subset of $B$, then

Generation conjecture. Conversely, any maximally monotone subspace $Mathcal M$ can be generated as

The geometry conjecture. There exist vectors $v_1,\ldots,v_m$ in $X$ such that

The shadow Douglas–Rachford splitting scheme involves a stepsize parameter $\lambda$ and a constant $L$ as in Theorem. Extended stepsize conjecture. Although the result was not pro…

Let $\mathcal H$ be the Hilbert space considered in the forward-backward algorithm, let $\Phi$ be the convex function defining the proximal mapping, let $B$ be the monotone cocoerc…

Let $X$ be a Banach space. An operator is said to be of type (BR) or of type (D) in the terminology of the source. Nonreflexive-space conjecture. Every nonreflexive space admits an…

Linear-relation sum conjecture. Then $A+B$ is maximally monotone. This conjecture is presented as a sufficient condition for an affirmative answer to the general sum problem for ma…