[Help-glpk] formulating svm

[Kaustubh Raosaheb Patil]

Hi,

I am trying to formulated a linear programming svm (support vector 
machine) using glpk. The problem is described as follows, given a set of 
observations X (a matrix with n rows and m columns) and a vector y with 
class labels {+1,-1} for each of the observations (n entries); find the 
following optimized solutions;

PRIMAL

minimize 0.5 * SUM{from j=1 to m} |wj|  - ( SUM{from i=1 to n} alphai * 
(yi*(w^T*xi - 1)) )

i and j indicate the vector/matrix elements
here vector w is the weight vector of length m
alpha is a vector of length n (Lagrange multipliers)

DUAL

maximize SUM{for i=1 to n} alphai - 0.5 * SUM{from i,j=1 to n} 
alphai*alphaj*yi*yj*(xi^T*xj)

subject to alphai >= 0 for i=1 to n

specifically I would like to use the R interface to glpk. I am not sure 
how these objective functions can be converted into a vector of 
coefficients.

Any suggestions are welcome.

best