Algorithm for Linear Least Squares Problems with Equality and Nonnegativity Constraints.

摘要

A new algorithm for solving a linear least-squares problem with linear constraints is presented. The constraints can be equality constraint equations and nonnegativity constraints on selected variables. This problem,while appearing to be quite special,is the core problem arising in the solution of the general linearly constrained linear least-squares problem. The reduction process of the general problem to the core problem can be done in many ways. Three such techniques are discussed. The method employed for solving the core problem is based on combining the equality constraints with differentially weighted least-squares equations to form an augmented least-squares system. This weighted least-squares system is solved with nonnegativity constraints on selected variables. Seven small examples,including a constrained least-squares curve fitting example,are presented. A reference to user instructions for subprograms to compute solutions of constrained least-squares problems is included. 3figures, 9tables. (ERA citation 04:017638)