thank you all for your help.
I have found that the MATLAB function lsqnonneg does exactly what I am looking for. I'm speculating that it follows a procedure similar to what vedenev and EnumaElish are suggesting.
If you don't mind, could you or somebody else explain that procedure in more detail? I have only minimal experience working with lagrange multipliers. I'm unfamiliar with SAS. I've been running my numbers through Matlab.
[SOLVED] Multivariate Linear Regression With Coefficient Constraint
I'm attempting a multivariate linear regression (mvlr) by method of least squares. Basically, I'm solving a matrix of the following form for \beta_p,
$ \begin{bmatrix} \sum y \\ \sum x_1 y \\ \sum x_2 y \\ \sum x_3 y...