22.214.171.124.27 LSLS is a solver for estimating linear regression models in GAMS. It solves the normal equations (X'X)b=X'y to introduce numerical instability. It was originally developed by Erwin Kalvelagen is the original author [sic] and further information can be found in the solver manual or at the Amsterdam Optimization Modeling Group's web site.
This statement is not completely correct. I surely don't want to solve the normal equations to introduce numerical instability. Actually I don't form the normal equations at all (for good reasons). The algorithm is based on a stable QR decomposition (see section 5 of LS solver documentation). The code has been verified to solve some very numerically challenging problems. Some users have used LS to solve regression problems with hundreds of coefficients to estimate.