Remove normalization by problem dimension

This is a proposal, see #169

If we don't do that, then we should update the documentation (formulae
and parallel with the SCS API).

Author: stephane-caron

include/proxsuite/proxqp/dense/utils.hpp

@@ -347,9 +347,6 @@ global_dual_residual(Results<T>& qpresults,
   // dual_feasibility_rhs_3 = norm(unscaled(CTz))
   //
   // dual_residual_scaled = scaled(Hx + g + ATy + CTz)
-  const isize max_dim =
-    std::max(qpmodel.dim, std::max(qpmodel.n_eq, qpmodel.n_in));
-  const T sqrt_max_dim(std::sqrt(max_dim)); // for normalizing scalar products
 
   qpwork.dual_residual_scaled = qpwork.g_scaled;
   qpwork.CTz.noalias() =
@@ -409,9 +406,6 @@ global_dual_residual(Results<T>& qpresults,
   duality_gap += zl;
 
   ruiz.scale_dual_in_place_in(VectorViewMut<T>{ from_eigen, qpresults.z });
-
-  duality_gap /= sqrt_max_dim; // in order to get an a-dimensional duality gap
-  rhs_duality_gap /= sqrt_max_dim;
 }
 
 } // namespace dense

include/proxsuite/proxqp/sparse/utils.hpp

@@ -637,9 +637,6 @@ unscaled_primal_dual_residual(
 {
   isize n = x_e.rows();
 
-  const isize max_dim = std::max(data.dim, std::max(data.n_eq, data.n_in));
-  const T sqrt_max_dim(std::sqrt(max_dim)); // for normalizing scalar products
-
   LDLT_TEMP_VEC_UNINIT(T, tmp, n, stack);
   dual_residual_scaled = qp_scaled.g.to_eigen();
   {
@@ -681,10 +678,6 @@ unscaled_primal_dual_residual(
     rhs_duality_gap = std::max(rhs_duality_gap, std::abs(zu));
 
     precond.scale_dual_in_place_in({ proxsuite::proxqp::from_eigen, z_e });
-
-    results.info.duality_gap /=
-      sqrt_max_dim; // in order to get an a-dimensional duality gap
-    rhs_duality_gap /= sqrt_max_dim;
   }
 
   {