Exponential cone convex programs fail to converge

[marcusps]

This prevents ML tomography from using a convex program formulation (thus the use of the iterative R \rho R algorithm) or the use of hedging. Moreover, SCS is the only solver I am aware of that can solve mixed semidefinite and exponential cone programs, and SCS is currently having issues even with pure SDP formulations of tomography.

Perhaps an alternative is to use projected gradient searches -- should be flexible enough to handle maximum likelihood, hedging, maximum entropy, etc.

[blakejohnson]

It shouldn't be related, but does the new support in Convex.jl for programs on complex variables make any difference?

[marcusps]

I haven't had a chance to look through that, but also wasn't entirely sure to what extent complex variables were supported. Last I looked it seemed not all atoms were supported, and not all convex programs were supported (I don't recall any mention of exponential cones).

It is worth a closer look, especially regarding the other issues with SCS.