  We introduce an extension to the Discrete Multiplier Method (DMM), called
Minimal $\ell_2$ Norm Discrete Multiplier Method (MN-DMM), where conservative
finite difference schemes for dynamical systems with multiple conserved
quantities are constructed procedurally, instead of analytically as in the
original DMM. For large dynamical systems with multiple conserved quantities,
MN-DMM alleviates difficulties that can arise with the original DMM at
constructing conservative schemes which satisfies the discrete multiplier
conditions. In particular, MN-DMM utilizes the right Moore-Penrose
pseudoinverse of the discrete multiplier matrix to solve an underdetermined
least-square problem associated with the discrete multiplier conditions. We
prove consistency and conservative properties of the MN-DMM schemes. We also
introduce two variants - Mixed MN-DMM and MN-DMM using Singular Value
Decomposition - and discuss their usage in practice. Moreover, numerical
examples on various problems arising from the mathematical sciences are shown
to demonstrate the wide applicability of MN-DMM and its relative ease of
implementation compared to the original DMM.
