  We present two globally convergent Levenberg-Marquardt methods for finding
zeros of H\"{o}lder metrically subregular mappings that may have non-isolated
zeros. The first method unifies the Levenberg- Marquardt direction and an
Armijo-type line search, while the second incorporates this direction with a
nonmonotone trust-region technique. For both methods, we prove the global
convergence to a first-order stationary point of the associated merit function.
Furthermore, the worst-case global complexity of these methods are provided,
indicating that an approximate stationary point can be computed in at most
$\mathcal{O}(\varepsilon^{-2})$ function and gradient evaluations, for an
accuracy parameter $\varepsilon>0$. We also study the conditions for the
proposed methods to converge to a zero of the associated mappings. Computing a
moiety conserved steady state for biochemical reaction networks can be cast as
the problem of finding a zero of a H\"{o}lder metrically subregular mapping. We
report encouraging numerical results for finding a zero of such mappings
derived from real-world biological data, which supports our theoretical
foundations.
