Algorithm 552: Solution of the Constrained I1 Linear Approximation Problem [F4]

TLDR: The algorithm can be used to solve the constrained 11 approximation problem and, if no vector x satisfying (2) and (3) exists, the subroutine detects this and informs the user that the problem is infeasible.

Abstract: subject to the given constraints (2) and (3). (In expression (4), b, denotes the ith component of b and A, denotes the ith row of A.) The method is completely general in the sense that no restrictions are imposed on the ranks of the matrices A, C, and E, or on the signs of the elements of f. Furthermore, if no vector x satisfying (2) and (3) exists, the subroutine detects this and informs the user that the problem is infeasible. The algorithm can be used to solve the constrained 11 approximation problem. Suppose that data consisting of k points (t , y,) are to be approximated by a linear