Polynomial data fitting that guarantees convexity

Hi there,

I have a dataset with N number of data points [x1, x2, ...., xN], [y1, y2, ..., yN]. I can use polyfit by providing the order of polynomial. But it doesn't guarantee that the polynomial is convex. Is there any way that I can find the best fitting polynomial but still guarantees convexity? Also, if I want to add constraint such as the polynomial passes through a specific data points or a number of specific points (still guarantees convexity), what would be the way?

Thanks,