Dax looks at two aspects of solving bounded linear least squares problems by the active set method: finding an initial starting point, and dropping active constraints to select the starting point for the next iteration. The author presents a useful technique for speeding up bounded linear least squares problems, and also shows some routes that do not pay off.

The paper works on using two simple iteration methods, Gauss-Seidel and projected gradient, to come up with an improved starting point, on the basis that it is cheaper to do this where possible than to perform the full calculations. The aim is to switch to the full calculations once the final active set has been found, which is deemed to be the case when the members of the active set do not change between a set number of iterations of the quick method.

Through numerical experiments, the paper shows that in almost all cases it is well worthwhile to use the Gauss-Seidel method to come up with a good initial starting point, and that this works significantly better than using the projected gradient method. For subsequent iterations this approach does not pay, however, despite the anticipated benefits of being able to modify several constraints for each iteration. Instead, it is better to use the standard method of removing one constraint at a time.