Does Orthogonal Matching Pursuit have the problem of divergence?

I am using the Matlab code of OMP to solve a nonlinear problem. But I do not now if OMP has the problem of divergence. As to my understanding, Matching Pursuit should not have the problem of divergence. Am I correct? If I am correct, does OMP have the problem of divergence?

Thanks a lot for your answers in advance. Happy Holidays!

Bei Gou