I have a set of data points $\{ (x_i,y_i) \}$. The target is to find a curve that fits these points best, so I use the least square method: $$ \min \sum_j^p| f(x_j)-y_j |^2 \\ \text{where } f(x) = a x + \sum_{i}^{n} b_i J_1(c_i x) $$ where $J_1$ is the first order Bessel function. I have to find a set consists of $(2n+1)$ parameters $\{ a, b_1, ... b_n, c_1, ..., c_n \}$ that minimize the residual function.
However, this problem was not a convex optimization problem so that had more than one local minimum. The fitting program will always converge to a local minimum point, which is annoying. I want to convert this optimization problem into a convex optimization problem. What should I do?