kernlab: ipop – R documentation

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ipop

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

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)

kernlab

Kernel-Based Machine Learning Lab

v0.9-29

GPL-2

Authors

Alexandros Karatzoglou [aut, cre], Alex Smola [aut], Kurt Hornik [aut], National ICT Australia (NICTA) [cph], Michael A. Maniscalco [ctb, cph], Choon Hui Teo [ctb]

Initial release