Potential typo when computing primal_feasibility_in_rhs_0 in global_primal_residual?

[oswinso]

I think maybe there is a typo when computing primal_feasibility_in_rhs_0 in the global_primal_residual function when there are box constraints?

proxsuite/include/proxsuite/proxqp/dense/utils.hpp

Lines 220 to 221 in c9586f8

	primal_feasibility_in_rhs_0 = std::max(
	primal_feasibility_in_rhs_0, infty_norm(qpresults.si.tail(qpmodel.dim)));

Mathematically, my understanding is that this is used for computing the relative errors, and should be

$$ \text{primal\_feasibility\_in\_rhs\_0} = \max\{ \lVert C x \rVert_{\infty}, \lVert x \rVert_{\infty} \} $$

However, the problem right now is that qpresults.si.tail(qpmodel.dim) does not contain $x$. It seems like this is not assigned in this function, and either contains zero or some other expression, i.e., from here

proxsuite/include/proxsuite/proxqp/dense/solver.hpp

Lines 980 to 981 in c9586f8

	// contains now : C(x+alpha dx)-l + z_prev * mu_in
	qpresults.si += alpha * Cdx;

This seems like a typo?

Perhaps it should instead be

primal_feasibility_in_rhs_0 = std::max(
      primal_feasibility_in_rhs_0, infty_norm(qpwork.primal_residual_in_scaled_up.tail(qpmodel.dim)));

which does contain $\lVert x \rVert_{\infty}$, as assigned from earlier in the function?

proxsuite/include/proxsuite/proxqp/dense/utils.hpp

Lines 196 to 200 in c9586f8

	qpwork.primal_residual_in_scaled_up.tail(qpmodel.dim) = qpresults.x;
	// qpwork.primal_residual_in_scaled_up.tail(qpmodel.dim).array() *=
	// qpwork.i_scaled.array();
	ruiz.unscale_primal_in_place(VectorViewMut<T>{
	from_eigen, qpwork.primal_residual_in_scaled_up.tail(qpmodel.dim) });

[Bambade]

Dear @oswinso,
Thanks a lot for reporting this typo. qpresults.si.tail(qpmodel.dim) was indeed not assigned at this stage.
There are several ways for computing relative errors. One usual way (adapted to the box constraint case) is to indeed use $||x||_\infty$ and also the norm of its projection onto the box constraints. I have added these two in PR #258.

[jcarpent]

Solved via #258.