I am working on some project in Matlab, where I defined some function $R(x, h, H, L, N)$ and I want to find such $h, H, L, N$ such that $R(x, h, H, L, N)$ is approximated by some sine wave in other words I want to find $\min_{h, H, L, N, a, b, c}| R(x, h, H, L, N) - (a\sin(bx)+c)|$ (function R takes some time to compute so I am looking for something less straight forward then just brute force method).
Before implementing anything like that I am interested if there is any theorey on such problem.