CVXGEN: Code Generation for Convex Optimization

Example: Support vector machine (SVM)

This example, from machine learning, demonstrates the creation of a support vector machine (SVM). For some more details, see Boyd and Vandenberghe, 8.6.1.

Optimization problem

We are given observations

$(x_i, y_i) in mathbf{R}^n times {-1,1}$ , for , and a parameter
$lambda in mathbf{R}_+$

We wish to choose two optimization variables: a weight vector

$w in mathbf{R}^{n}$ , and offset

to solve the optimization problem

$begin{array}{ll} mbox{minimize} & |w|_2^2 + lambda sum_{i=1,ldots,N} left( 1 - y_i(w^T x_i - b) right)_+ end{array}$

CVXGEN code

dimensions
  N = 50  # observations.
  n = 10  # support vector dimension.
end

parameters
  x[i] (n), i=1..N
  y[i], i=1..N
  lambda positive
end

variables
  w (n)  # weight vector.
  b  # offset.
end

minimize
  quad(w) + lambda*sum[i=1..N](pos(1 - y[i]*(w'*x[i] - b)))
end