1. A computer-implemented non-linear optimizer for use with a limited precision computer processor executing a calling procedure that generates a plurality of model parameters and requests a solution to a non-linear model from the non-linear optimizer, comprising: means for initializing a non-linear model by forming an objective function (F) having one or more functional components (F 1 , F 2 ,. .. ) and a marginal variance matrix (V) using a plurality of input parameters to the model stored in a memory coupled to the processor; wherein the objective function (F) can be described in terms of the marginal variance matrix (V) without requiring calculus integrating operations on the marginal variance matrix (V); means for iteratively solving the non-linear model using the computer processor until the model has converged to a feasible solution, comprising: means for evaluating the feasibility of computing the objective function by determining if the marginal variance matrix (V) is positive definite, thereby indicating whether the limited precision processor is capable of calculating a feasible solution to the objective function; means, responsive to the marginal variance matrix (V) being positive definite, for executing a first set of computer software instructions using the limited precision computer processor that calculate the objective function (F) and its gradient using the marginal variance matrix (V); and means, responsive to the marginal variance matrix (V) not being positive definite, for executing a second set of computer software instructions using the limited precision computer processor that: (a) construct a surrogate marginal variance matrix (V+) that is positive definite; (b) construct a surrogate objective function (F+) in which the one or more functional components (F 1 , F 2 ,. .. ) of the objective function are replaced with surrogate functional components (F 1 +, F 2 +,. .. ) having continuous first derivatives; and (c) calculate the surrogate objective function (F+) and its gradient using the surrogate marginal variance matrix (V+).