How do I formulate soft margin SVM in primal form for quadprog function?

I am not able to formulate the matrices needed for quadprog function to solve soft margin SVM.

Answer 1

[Nitin Khola]

My answer is based on the following Wikipedia article and documentation links. Refer to these links for notation related questions: https://en.wikipedia.org/wiki/Support_vector_machine#Soft_margin. http://www.mathworks.com/help/optim/ug/quadprog.html

For the objective function, you just need need the H to be [1 0 0; 0 0 0; 0 0 0] assuming each of w,eta, and b are scalar quantities. In order to generalize this idea for vector w,eta, and b. You need H to be a multidimensional array so that the dimensions match when you are trying to do [w' eta' b']*H*[w eta b]. Another quantity required is "f" and it should be of the form [0; c; 0].

The constraints are linear as well. You can follow a similar method for setting up the constraints. Hope it helps!