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Constrained regression

Dear Carlos,

One approach is to use structural equation modeling (SEM). Some SEM
packages, such as LISREL, Mplus and Mx, allow inequality and nonlinear
constraints. Phantom variables (Rindskopf, 1984) may be used to impose
inequality constraints. Your model is basically:
y = b0 + b1*b1*x1 + b2*b2*x2 +...+ bp*bp*xp + e
1 = b1*b1 + b2*b2 +...+ bp*bp

Alternatively, you can set some condition bounds on the parameter
estimates. Then you only have to impose the second constraint.

Rindskopf, D. (1984). Using phantom and imaginary latent variables to
parameterize constraints in linear structural models. Psychometrika,
49, 37-47.

Regards,
Mike