Decide whether subspace inversion is the right strategy for singular Jacobians

Determine whether inverting the Jacobian only on its image (ignoring the null space) when the Jacobian is singular is the right choice for the multidimensional Newton–Raphson marginal price algorithm, by analyzing its effect on convergence and runtime relative to alternatives such as termination or different regularizations.

Background

In higher dimensions, the authors sometimes encounter singular Jacobians when applying their marginal price (Newton–Raphson) method. Their current fallback is to invert the Jacobian on its image only, hoping to return to a non-singular region.

They explicitly note uncertainty about whether this strategy is optimal, as it may waste iterations if the algorithm does not quickly re-enter a region where the full Jacobian is invertible.