  We design a homotopy continuation algorithm, that is based on numerically
tracking Viro's patchworking method, for finding real zeros of sparse
polynomial systems. The algorithm is targeted for polynomial systems with
coefficients satisfying certain concavity conditions. It operates entirely over
the real numbers and tracks the optimal number of solution paths. In more
technical terms; we design an algorithm that correctly counts and finds the
real zeros of polynomial systems that are located in the unbounded components
of the complement of the underlying A-discriminant amoeba.
