Constrained least squares

In constrained least squares one solves a linear least squares problem with an additional constraint on the solution. This means, the unconstrained equation X β = y {\displaystyle \mathbf {X} {\boldsymbol {\beta }}=\mathbf {y} } must be fit as closely as possible (in the least squares sense) while ensuring that some other property of β {\displaystyle {\boldsymbol {\beta }}} is maintained.