Solving the minimal least squares problem subject to bounds on the variables.

*(English)*Zbl 0546.65041The author considers a solution method for linear least squares problems subject to lower and upper bounds on the variables. In a first step, an arbitrary solution is found based on an active set strategy. The corresponding subproblems are either solved by direct factorization (QR) or a conjugate gradient method. Subsequently the minimum norm solution of the least squares problem is determined. The algorithm and details on its numerical implementation are outlined and some numerical results are presented.

Reviewer: K.Schittkowski

##### MSC:

65K05 | Numerical mathematical programming methods |

90C20 | Quadratic programming |

62J05 | Linear regression; mixed models |

65H10 | Numerical computation of solutions to systems of equations |

##### Keywords:

linear least squares problems; active set strategy; direct factorization; conjugate gradient method; minimum norm solution; numerical results
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##### References:

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