An Algorithm for a Restricted Discrete Approximation Problem in the $L_1 $ Norm

Discrete approximation problems in the $L_1 $ norm arise in fitting by polynomials, linear regression, and goal programming. This paper presents an algorithm to solve discrete approximations in the $L_1 $ norm when the parameters are restricted by linear constraints. The algorithm is a special purpose primal linear programming method that utilizes certain properties of the problem to substantially reduce storage requirements and solution times. Computational experience with a computer code version of the algorithm will be presented.