The primary problem of the soft-margin SVM with the linear kernel is given by minw,b, s.t. 21w2+Ci=1niyi(wxi+b)1i,i0,i=1,,n. - Use the Lagrangian dual theory to prove that its dual problem is given by min s.t. i=1ni+21i,j=1nijyiyjxi,xji=1nyii=0,0iC. - Show that both the primal problem (1) and the dual problem (2) are convex. - Starting from the dual problem for the linear SVM, describe how the above linear SVM formulation is extended to the nonlinear case..

1. The primary problem of the soft-margin SVM with the linear kernel is given by minw,b, s.t.
21w2+Ci=1niyi(wxi+b)1i,i0,i=1,,n. - Use the Lagrangian dual theory to prove that its dual
problem is given by min s.t. i=1ni+21i,j=1nijyiyjxi,xji=1nyii=0,0iC. - Show that both the primal
problem (1) and the dual problem (2) are convex. - Starting from the dual problem for the linear
SVM, describe how the above linear SVM formulation is extended to the nonlinear case.