  Implementations in R of classical general-purpose algorithms for local
optimization generally have two major limitations which cause difficulties in
applications to complex problems: too loose convergence criteria and too long
calculation time. By relying on a Marquardt-Levenberg algorithm (MLA), a
Newton-like method particularly robust for solving local optimization problems,
we provide with marqLevAlg package an efficient and general-purpose local
optimizer which (i) prevents convergence to saddle points by using a stringent
convergence criterion based on the relative distance to minimum/maximum in
addition to the stability of the parameters and of the objective function; and
(ii) reduces the computation time in complex settings by allowing parallel
calculations at each iteration. We demonstrate through a variety of cases from
the literature that our implementation reliably and consistently reaches the
optimum (even when other optimizers fail), and also largely reduces
computational time in complex settings through the example of maximum
likelihood estimation of different sophisticated statistical models.
