12 problems

The consensus model assumes a separable objective of the form $\sum_j f_j(\mathbf{x}_j,\mathbf{y}_j)$, with each term depending only on agent $j$'s own variables. In the non-separa…

Consider the six semidefinite programs in Group II of Experiment II, namely 1dc1024, G40mb, hand, neosfbr25, r12000, and swissroll, and let $\sigma$ denote the ADMM penalty paramet…

Let $\overline{Z}$ be the final convergent point of the iterations of one-step ADMM. Let $\mathcal{C}(\overline{Z})$ be the cone used in the local second-order analysis, and let…

Let $\overline{Z}$ be a reference point, let $\mathcal{C}(\overline{Z})$ denote the cone appearing in the local second-order ADMM analysis, and let…

Let TOP-ADMM generate sequences for the nonconvex problem $\texttt{P3}$, and let a KKT point mean a point satisfying the dual-feasibility and primal-feasibility conditions for the…

Let $\texttt{P3}$ be the paper's nonconvex optimization problem with iteration-dependent convexified PAPR and ACLR constraint sets, and let TOP-ADMM denote the corresponding algori…

NysADMM linear convergence conjecture. A modification of the authors' argument should show that NysADMM converges linearly for any strongly convex loss.

Let $\tau_A$ and $\tau_G$ denote the asymptotic convergence rates of distributed ADMM and gradient descent, respectively, and let $\tau_A^a$ and $\tau_G^a$ denote their optimal rat…

Consider the quadratic objective referred to in the source and an arbitrary graph $\mathcal{G}$. Let $\tau_G^\star$ and $\tau_A^\star$ be the optimal convergence rates of gradient…

Let a finite Markov chain be lifted to an expanded state space, and let the corresponding distributed over-relaxed ADMM algorithm be viewed as a lifting of gradient descent (GD) fo…

The setting is a class of problems for which cyclic ADMM with at least three blocks is convergent, such as certain strongly convex problems. Here ALM denotes the Augmented Lagrangi…

Consider the online setting described above, with convergence bounds of order $\mathcal{O}((s+r)p\log p/T+\alpha^2/p)$ when $\beta(p)=\Theta(\sqrt{p})$, and of order…