Description Usage Arguments Value References See Also Examples

This routine implements the dual method of Goldfarb and Idnani (1982,
1983) for solving quadratic programming problems of the form
*min(-d^T b + 1/2 b^T D b)* with the
constraints *A^T b >= b_0*.

1 |

`Dmat` |
matrix appearing in the quadratic function to be minimized. |

`dvec` |
vector appearing in the quadratic function to be minimized. |

`Amat` |
matrix defining the constraints under which we want to minimize the quadratic function. |

`bvec` |
vector holding the values of |

`meq` |
the first |

`factorized` |
logical flag: if |

a list with the following components:

`solution` |
vector containing the solution of the quadratic programming problem. |

`value` |
scalar, the value of the quadratic function at the solution |

`unconstrained.solution` |
vector containing the unconstrained minimizer of the quadratic function. |

`iterations` |
vector of length 2, the first component contains the number of iterations the algorithm needed, the second indicates how often constraints became inactive after becoming active first. |

`Lagrangian` |
vector with the Lagragian at the solution. |

`iact` |
vector with the indices of the active constraints at the solution. |

D. Goldfarb and A. Idnani (1982). Dual and Primal-Dual Methods for Solving Strictly Convex Quadratic Programs. In J. P. Hennart (ed.), Numerical Analysis, Springer-Verlag, Berlin, pages 226–239.

D. Goldfarb and A. Idnani (1983).
A numerically stable dual method for solving strictly convex quadratic
programs.
*Mathematical Programming*, **27**, 1–33.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | ```
##
## Assume we want to minimize: -(0 5 0) %*% b + 1/2 b^T b
## under the constraints: A^T b >= b0
## with b0 = (-8,2,0)^T
## and (-4 2 0)
## A = (-3 1 -2)
## ( 0 0 1)
## we can use solve.QP as follows:
##
Dmat <- matrix(0,3,3)
diag(Dmat) <- 1
dvec <- c(0,5,0)
Amat <- matrix(c(-4,-3,0,2,1,0,0,-2,1),3,3)
bvec <- c(-8,2,0)
solve.QP(Dmat,dvec,Amat,bvec=bvec)
``` |

```
$solution
[1] 0.4761905 1.0476190 2.0952381
$value
[1] -2.380952
$unconstrained.solution
[1] 0 5 0
$iterations
[1] 3 0
$Lagrangian
[1] 0.0000000 0.2380952 2.0952381
$iact
[1] 3 2
```

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