Documentation on convex solvers confusing

[rileyjmurray]

One page says that Elemental's convex solvers are based on the Mehrotra predictor–corrector method.

But another page says they are based on ADMM.

ADMM and Mehrotra's predictor-corrector method are very different. Indeed, both are primal-dual solvers, but ADMM is considered "first order" while the predictor-corrector method is "second order". It seems to me that the sentence

Elemental currently supports distributed dense and sparse Linear, Quadratic, and Second-Order Cone Programs via Mehrotra Predictor-Corrector primal-dual Interior Point Methods

from the first link should simply be updated to

Elemental currently supports distributed dense and sparse Linear, Quadratic, and Second-Order Cone Programs via ADMM.

[poulson]

Hi Riley,

There is indeed code for primal dual IPMs, though the stability of the numerics across the range of precisions is something I stopped working on.

[poulson]

Please see https://github.com/elemental/Elemental/tree/master/src/optimization/solvers

[poulson]

Again, the numerics is in flux (nearly resolved even for infinite precision in a branch), but I haven't worked on this project in nearly two years.

[rileyjmurray]

I see. Thank you for the explanation!