Least squares with inequality restrictions: a symmetric positive-definite linear complementarity problem algorithm

Abstract

When finding the least squares estimate in a full rank regression subject to inequality constraints, a symmetric positive-definite linear complementarity problem is encountered if the set of linear constraints is full rank.

This particular problem is analyzed here, and an algorithm is proposed. A comparison is done between this algorithm and Lemke’s algorithm. An Apple II microcomputer is used for the comparison.

Keywords:

• Least Squares
• Linear Complementarity

†tpresently at the Department of Statistics, University of Warwick, Coventry CV4 7AL, UK.

†tpresently at the Department of Statistics, University of Warwick, Coventry CV4 7AL, UK.

Notes

†tpresently at the Department of Statistics, University of Warwick, Coventry CV4 7AL, UK.