  We evaluate and extend the solution methods for models with binary and
multiple continuous choice variables in dynamic programming, particularly in
cases where a discrete state space solution method is not viable. Therefore, we
approximate the solution using taste shocks or black-box optimizers that
applied mathematicians use to benchmark their algorithms. We apply these
methods to a default framework in which agents have to solve a portfolio
problem with long-term debt. We show that the choice of solution method
matters, as taste shocks fail to attain convergence in multidimensional
problems. We compare the relative advantages of using four optimization
algorithms: the Nelder-Mead downhill simplex algorithm, Powell's direction-set
algorithm with LINMIN, the conjugate gradient method BOBYQA, and the
quasi-Newton Davidon-Fletcher-Powell (DFPMIN) algorithm. All of these methods,
except for the last one, are preferred when derivatives cannot be easily
computed. Ultimately, we find that Powell's routine evaluated with B-splines,
while slow, is the most viable option. BOBYQA came in second place, while the
other two methods performed poorly.
