I am working on a quadratic conic optimization problem, but I have discovered that it would be preferrable if the quadratic constraint is linearly approximated. In other words, I need some way to make the quadratic beta variable linear. Is there any good way to do this? The only decision variable here is the beta, everything else is given as inputs to the problem.
I have thought about maybe using Taylor expansion, but this needs to be around a point A so I am not quite sure how it would work. Would I need to divide the original quadratic constraint into piecewise constraints based on the value of the beta?