I am attempting to build a model a for which the only valid output in the range [0,100]. I was wondering if would be possible to reduce the penalty on values under 0 and over 100 as they will be constrained anyway in order to get a better fit.
If I understand you correctly, this model can be fitted using logit ideas.
Scale your response by dividing by 100. Then use an appropriate generalised linear model for proportional or fractional responses. There is an accessible miniature review at http://www.stata-journal.com/sjpdf.html?articlenum=st0147 although the ideas are older than there implied. Bartlett was taking logits of proportions back in 1937.
This is easy in Stata and no doubt in any major statistical environment.
However, I think you are wrong: this can't, or shouldn't, be standard least squares regression as any hyperplane predicts values for the response outside a bounded range, even if the prediction is bounded for your data points.