This paper suggests mathematical programming methods for estimating the parameters of piecewise regression models. Maximum likelihood estimation results in a non-convex optimization problem which is not continuously differentiable, and might even become discontinuous. To solve these difficulties we suggest two classes of methods. The first one consists of 'scanning methods', which are combinatorial in nature and therefore adequate for problems limited in size. The second class consists of 'smoothing (or approximation) methods', which can be used for larger problems. While scanning methods always find the global solution in a finite number of steps, smoothing methods are only guaranteed to find a local optimum. The paper ends with an application of the methods to the determination of export prices.