Because the Euclidean norm is defined as the square root of a sum of squares. You can drop the square root and calculate everything as a least squares optimization problem. This problem in turn can be solved by finding where the derivative of the quadratic function is zero. The derivative of a quadratic function is a linear function. This means it is possible to find a matrix decomposition, say QR decomposition, and solve the problem directly.

If you want non linear optimization, your best bet is sequential quadratic programming. So even in that case you're still doing quadratic programming with extra steps.