  A practical challenge for structural estimation is the requirement to
accurately minimize a sample objective function which is often non-smooth,
non-convex, or both. This paper proposes a simple algorithm designed to find
accurate solutions without performing an exhaustive search. It augments each
iteration from a new Gauss-Newton algorithm with a grid search step. A finite
sample analysis derives its optimization and statistical properties
simultaneously using only econometric assumptions. After a finite number of
iterations, the algorithm automatically transitions from global to fast local
convergence, producing accurate estimates with high probability. Simulated
examples and an empirical application illustrate the results.
