1. A computer-implemented system, including a 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: one or more computer-readable storage mediums containing software instructions executable on the limited precision computer processor to cause the limited precision computer processor to perform operations including: initializing the non-linear model by forming an objective function (F) having functional components (F 1 , F 2 , F 3. .. ) and a marginal variance matrix (V) using a plurality of input parameters to the model stored in a memory coupled to the limited precision computer processor; wherein the objective function (F) is described in terms of the marginal variance matrix (V), and wherein the marginal variance matrix (V) comprises a plurality of eigenvalues based on the input parameters to the model; iteratively solving the non-linear model using the limited precision computer processor until the model has converged to a feasible solution, comprising: 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 evaluating the feasible solution to the objective function; responsive to the marginal variance matrix (V) being positive definite, 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 responsive to the marginal variance matrix (V) not being positive definite, executing a second set of computer software instructions using the limited precision computer processor that: construct a surrogate marginal variance matrix (V + ) that is positive definite; construct a surrogate objective function (F + ) in which the functional components (F 1 , F 2 , F 3. .. ) of the objective function are replaced with surrogate functional components (F 1 + , F 2 + , F 3 + ,. .. ) having continuous first derivatives; calculate the surrogate objective function (F + ) and its gradient using the surrogate marginal variance matrix (V + ); and storing the objective function and its gradient or the surrogate objective function and its gradient.