Harmonic generation is an attractive research field that finds a variety of application areas. However, harmonic generation within a medium of micron-scale interaction length limits the magnitude of nonlinear coupling and leads to poor harmonic generation efficiency. In this study, we present a constrained non-linear programming approach based on the Quasi-Newton Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm to obtain high-fidelity harmonic generation in optical micro-resonators. Using this approach, one can achieve high-intensity harmonic generation in a simple Fabry-Perot type optical micro-resonator. The generation of super-intense harmonics at a typical ultraviolet (UV)-ablation frequency of 820 THz and at pure yellow-light (515 THz) is investigated in particular. Moreover, we achieved more than 98% accuracy compared to well-known theoretical results. Our approach enables the design of highly efficient microscale harmonic generators to be used in integrated photonic devices.