  The least absolute shrinkage and selection operator (lasso) and ridge
regression produce usually different estimates although input, loss function
and parameterization of the penalty are identical. In this paper we look for
ridge and lasso models with identical solution set.
  It turns out, that the lasso model with shrink vector $\lambda$ and a
quadratic penalized model with shrink matrix as outer product of $\lambda$ with
itself are equivalent, in the sense that they have equal solutions. To achieve
this, we have to restrict the estimates to be positive. This doesn't limit the
area of application since we can easily decompose every estimate in a positive
and negative part. The resulting problem can be solved with a non negative
least square algorithm.
  Beside this quadratic penalized model, an augmented regression model with
positive bounded estimates is developed which is also equivalent to the lasso
model, but is probably faster to solve.
