5 problems

Activity-identification conjecture. The finite-time activity-identification result proved by Liang, Fadili, and Peyré for constant step sizes should continue to hold for varying st…

The paper studies stochastic algorithms for sharp primal-dual problems, including linear programming, and proposes a variance-reduced method with restart. Optimal-rate conjecture.…

Small-disagreement conjecture. Small disagreements between the dual variables $\mu^1$ and $\mu^2$ should lead to small distances between the minima of $L(\cdot,\mu^1)$ and…

PDMM nonsingularity conjecture. At least for a subclass (e.g., the maximum-likelihood problem) of the optimization problem, the matrix set $\mathcal{P}$ might not need to be nonsin…

The primal-dual evolution involves a primal variable $u$ and a dual variable $\xi$, subject to a constraint on $\xi$. Convergence conjecture. Supported by numerical evidence, whene…