It also uses a similar idea to the convex optimization paper (to find the "dual" problem and try to solve it) so I would guess it has similar issues:
- Very very VERY complex to code, compared to e.g. PCG - Although it is asymptotically faster, the constant terms that you have to amortize might be very large. For instance, imagine you can sort on O(n) instead of on O(n log n) but the constant on the first case is a thousand times larger than on the second.
All in all, I am very interested about it, but you will need some valiant efforts in order to implement it efficiently.
"Convex minimization has applications in a wide range of disciplines, such as automatic control systems, estimation and signal processing, communications and networks, electronic circuit design, data analysis and modeling, statistics (optimal design), and finance."
I wonder if we could use convex optimization techniques to solve non convex problems (and occasionally jump out of local minima traps?)