12 problems

Let $p_1,p_2,p_3$ denote the first three parameter regimes in the sublinear convergence result for DCA, and let $N$ be the number of iterations. Exact-rate conjecture. The DCA rate…

Geometric interpolation conjecture. For all $\mathcal{K}>0$, $\kappa_1,\kappa_2>0$, and $\theta\in[0,1]$, the mixed-conditioning performance satisfies

Let $f$ and $g$ belong to the function classes $\mathcal{F}_{\rho,\alpha^{-1}}$ and $\mathcal{F}_{\mu,\beta^{-1}}$, respectively, and consider the optimization problem … Here GM, F…

Closed-form worst-case conjecture. The worst-case performance satisfies

Let $\mathcal{C}_{\mu_g}^{0}$ and $\mathcal{D}_{\mu_g}^{\mu_M}$ be the operator-composed function classes defined in the source, and let $\mathcal{C}_{\mu_g}^{0,(1)}$ and…

Let $N\geq 0$, $h\in[0,2]$, and let $\mathcal{F}_{\mu_f}$ be the class of functions with the smoothness and strong-convexity parameters specified in the source. Let…

OBL-G$_\flat$'s $\mathcal{A}^\star$-optimality conjecture. OBL-G$_\flat$ is $\mathcal{A}^\star$-optimal in the sense that

Let $(f,h)$ belong to the class $\mathcal{B}_L(C)$ of pairs satisfying the general $h$-smoothness assumptions, and consider IGA with a step size in $(0,1/L]$. IGA nonconvergence co…

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…

Composite-gradient FPGM conjecture. The solution $\hat{{\bm{h}}}_{\mathrm{D'}}$ corresponds to the coefficients defined by the FPGM construction in with the above choice of $t_i$.

FISTA global-minimizer conjecture. The feasible point with $t_i^2=T_i$ that corresponds to FPGM (FISTA) is a global minimizer of the relaxed problem defining…