  In this article we propose a shooting algorithm for partially-affine optimal
control problems, this is, systems in which the controls appear both linearly
and nonlinearly in the dynamics. Since the shooting system generally has more
equations than unknowns, the algorithm relies on the Gauss-Newton method. As a
consequence, the convergence is locally quadratic provided that the derivative
of the shooting function is injective and Lipschitz continuous at the optimal
solution. We provide a proof of the convergence for the proposed algorithm
using recently developed second order sufficient conditions for weak optimality
of partially-affine problems. We illustrate the applicability of the algorithm
by solving an optimal treatment-vaccination epidemiological problem.
