Convenience API for QPs

[mblondel]

Currently, the interface for QPs is like this:

params_obj = (Q, c)
params_eq = (A, b)
params_ineq = (G, h)

osqp = jaxopt.OSQP()
osqp.run(init, params_obj, params_eq, params_ineq)

I propose that we also add the following convenience API:

def guaranteed_quadratic_function(params, params_obj):
   [...]

osqp = jaxopt.OSQP(fun=guaranteed_quadratic_function)
osqp.run(init, params_obj, params_eq, params_ineq)

The idea is that we can, internally, automatically compute Q and c for the user using AD

grad = jax.grad(self.fun)
c = grad(zeros, params_obj)
Q = jax.jacobian(grad)(zeros, params_obj)

Similarly, for solvers like OSQP that can leverage matvecs, we can derive the matvec of Q automatically.

CC @Algue-Rythme

[mblondel]

or maybe

def guaranteed_quadratic_function(params, *params_obj):
   [...]

instead

[Algue-Rythme]

Good idea, I will take a look !

[mblondel]

This is now done for OSQP! Keeping the issue open as it also need to be done for CvxpyQP, EqQP, BoxCDQP and it needs to be documented.