An algorithm for estimating the parameters in multiple linear regression model with linear constraints

This paper develops an algorithm for estimating the parameters when the parameters are restricted by linear constraints in a general multiple regression model. The algorithm solves discrete approximation in the Φ error where Φ is a convex and symmetric function. These discrete approximations arise in fitting by polynomials, linear regression and goal programming. Discrete approximation problems in the L1 norm is a special case. The approaches to the solution of these approximation problems have a long history. The algorithm utilizes certain properties of the problem to significantly reduce the number of iterations to find the approximated solution.