  We construct triaxial dynamical models for the Milky Way nuclear star cluster
using Schwarzschild's orbit superposition technique. We fit the stellar
kinematic maps presented in Feldmeier et al. (2014). The models are used to
constrain the supermassive black hole mass M_BH, dynamical mass-to-light ratio
M/L, and the intrinsic shape of the cluster. Our best-fitting model has M_BH =
(3.0 +1.1 -1.3)x10^6 M_sun, M/L = (0.90 +0.76 -0.08) M_sun/L_{sun,4.5micron},
and a compression of the cluster along the line-of-sight. Our results are in
agreement with the direct measurement of the supermassive black hole mass using
the motion of stars on Keplerian orbits. The mass-to-light ratio is consistent
with stellar population studies of other galaxies in the mid-infrared. It is
possible that we underestimate M_BH and overestimate the cluster's triaxiality
due to observational effects. The spatially semi-resolved kinematic data and
extinction within the nuclear star cluster bias the observations to the near
side of the cluster, and may appear as a compression of the nuclear star
cluster along the line-of-sight. We derive a total dynamical mass for the Milky
Way nuclear star cluster of M_MWNSC = (2.1 +-0.7)x10^7 M_sun within a sphere
with radius r = 2 x r_eff = 8.4 pc. The best-fitting model is tangentially
anisotropic in the central r = 0.5-2 pc of the nuclear star cluster, but close
to isotropic at larger radii. Our triaxial models are able to recover complex
kinematic substructures in the velocity map.
