JuliaFirstOrder
Projection on polyhedral set
It would be nice to have it there. I mean for general polyhedral sets lb<=A*x<=ub xmin<=x<=xmax
It could either be implemented by calling an external QP solver or solve the dual using e.g., PANOC. Also there should be an option to warm-start the whole thing.
This could this be an instance of the more general case g(x) = f(Ax), for convex, proximable f, I guess.
Even better, although you wouldn't be able to use a QP solver for the prox of f(Ax), only dual PANOC (NAMA). But if it is a QP, then we should be able to have the option to use something like GUROBI for small problems.
I just submitted a paper for a QP solver. It is supposed to be really efficent projecting on Ax=b, Cx<=d, when the set of constraints is relatively small, by solving the dual problem. The algorithm, completely in julia is found here: https://github.com/mfalt/QPDAS.jl We could add it as an option for "solver". The interface is almost the same, we would have to rewrite when lower bound is equal to upper bound to an equality, and there is no added efficiency for using xmin/xmax instead of lb/ub. And it allows for any of these bounds to be changed without re-factorizing, and warmstart is done automatically.
It should beat OSQP pretty comfortably unless the number of inequalites is large.
