12 problems

In the convex composite problem with closed proper convex functions $f,g$, suppose the Douglas–Rachford operator has a fixed point $w^\star$ and $f$ is $L$-smooth. Let $\rho$ denot…

Consider the convex composite problem … where $f$ and $g$ are closed proper convex functions. Assume that the Douglas–Rachford operator has a fixed point $w^\star$, that $f$ is $L$…

Let $A$ and $B$ be operators satisfying the paper's standing Assumption, let $B$ be $\beta$-cocoercive, and let $A=\partial g$ for a closed proper convex function $g$. Let…

Consider the Davis–Yin splitting method and the ergodic primal–dual gap bound established in Theorem \mathrm{dys\text{-}gf\text{-}conv), whose rate is…

Let $\{y^k\}$ be the shadow sequence generated in the comonotone Douglas--Rachford framework, with parameters $\alpha$ and $\beta$. Strong convergence conjecture. The shadow sequen…

Fractional-regularity convergence conjecture. This assumption should lead to a solution

Let Set1 be the parameter set considered in the numerical experiments, let the small region of interest (ROI) lie close to the early exercise region (EER), and let the option value…

Let $S^\star\in\mathbb{R}^{3\times 3}$ denote an optimal solution of the dual operator-splitting performance estimation problem. Low-rank dual solution conjecture. The optimal solu…

Let the primal operator-splitting performance estimation problem be solved symbolically, and let the worst-case operators denote operators attaining its worst-case contraction fact…

Consider a convex optimization problem with primal optimal value $p^\star$ and dual optimal value $d^\star$, and let $x^{k+1/2}$ and $x^{k+1}$ denote the successive Douglas–Rachfor…

The IDC-OS methods approximate the residual integral in their error equation using quadrature nodes; in the simulations described here, 13 uniformly distributed interior nodes are…

Improved velocity error estimates conjecture. Both error estimates can be improved by a factor of $\tau^{\frac12}$, irrespective of the space dimension.