R: Quadratic Programming Solver

ipop {kernlab} | R Documentation

## Quadratic Programming Solver

### Description

ipop solves the quadratic programming problem :
\min(c'*x + 1/2 * x' * H * x)
subject to:
b <= A * x <= b + r
l <= x <= u

### Usage

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

### Arguments

`c` | Vector or one column matrix appearing in the quadratic function
`H` | square matrix appearing in the quadratic function, or the decomposed form Z of the H matrix where Z is a n x m matrix with n > m and ZZ' = H.
`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

### Details

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.

### Value

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)

### Author(s)

Alexandros Karatzoglou (based on Matlab code by Alex Smola)
alexandros.karatzoglou@ci.tuwien.ac.at

### References

R. J. Vanderbei
LOQO: An interior point code for quadratic programming
Optimization Methods and Software 11, 451-484, 1999
http://www.princeton.edu/~rvdb/ps/loqo5.pdf

### See Also

`solve.QP`, `inchol`, `csi`

### Examples

    ## 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)

[Package kernlab version 0.9-25 Index]