A concurrent learning adaptive-optimal control architecture is presented that combines learning-focused direct adaptive controllers with model predictive control for guaranteeing safety during adaptation for nonlinear systems. Exponential parameter convergence properties of concurrent learning adaptive controllers are leveraged to learn a feedback linearization signal that reduces a nonlinear system to an approximation of a linear system for which an optimal solution is known or can be easily computed online. Stability of the overall architecture is analyzed, and numerical simulations on a wing-rock dynamics model are presented in presence of significant system uncertainty, parameter variation, and measurement noise.