ipop | R Documentation |

ipop solves the quadratic programming problem :

*\min(c'*x + 1/2 * x' * H * x)*

subject to:

*b <= A * x <= b + r*

*l <= x <= u*

ipop(c, H, A, b, l, u, r, sigf = 7, maxiter = 40, margin = 0.05, bound = 10, verb = 0)

`c` |
Vector or one column matrix appearing in the quadratic function |

`H` |
square matrix appearing in the quadratic function, or the
decomposed form |

`A` |
Matrix defining the constrains under which we minimize the quadratic function |

`b` |
Vector or one column matrix defining the constrains |

`l` |
Lower bound vector or one column matrix |

`u` |
Upper bound vector or one column matrix |

`r` |
Vector or one column matrix defining constrains |

`sigf` |
Precision (default: 7 significant figures) |

`maxiter` |
Maximum number of iterations |

`margin` |
how close we get to the constrains |

`bound` |
Clipping bound for the variables |

`verb` |
Display convergence information during runtime |

ipop uses an interior point method to solve the quadratic programming
problem.

The *H* matrix can also be provided in the decomposed form *Z*
where *ZZ' = H* in that case the Sherman Morrison Woodbury formula
is used internally.

An S4 object with the following slots

`primal` |
Vector containing the primal solution of the quadratic problem |

`dual` |
The dual solution of the problem |

`how` |
Character string describing the type of convergence |

all slots can be accessed through accessor functions (see example)

Alexandros Karatzoglou (based on Matlab code by Alex Smola)

alexandros.karatzoglou@ci.tuwien.ac.at

R. J. Vanderbei

*LOQO: An interior point code for quadratic programming*

Optimization Methods and Software 11, 451-484, 1999

https://vanderbei.princeton.edu/ps/loqo5.pdf

`solve.QP`

, `inchol`

, `csi`

## solve the Support Vector Machine optimization problem data(spam) ## sample a scaled part (500 points) of the spam data set m <- 500 set <- sample(1:dim(spam)[1],m) x <- scale(as.matrix(spam[,-58]))[set,] y <- as.integer(spam[set,58]) y[y==2] <- -1 ##set C parameter and kernel C <- 5 rbf <- rbfdot(sigma = 0.1) ## create H matrix etc. H <- kernelPol(rbf,x,,y) c <- matrix(rep(-1,m)) A <- t(y) b <- 0 l <- matrix(rep(0,m)) u <- matrix(rep(C,m)) r <- 0 sv <- ipop(c,H,A,b,l,u,r) sv dual(sv)

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