Does an SVM classifier with a training error of 0 necessarily exist?
In theory, there is a set of parameters 
, and 
such that SVM training error is zero, but this is not necessarily a parameter SVM solution satisfies the conditions, when the actual training SVM model, will join a slack variable, it is also possible to ensure an SVM classifier obtained Is it satisfied that the training error is 0?
Therefore, we need to find a set of parameters so that the training error is 0 and the solution of the SVM model.
Solutions SVM model constraints are 
now we get a set of parameters that can, when 
, the 
; as 
when 
.
Therefore, we also need to meet the conditions, 
therefore, for a formula, first make b = 0, then 
therefore, 
here 
. If the value is very small, it is enough 
. At this time, the solution condition of SVM is satisfied, and the model error is also 0 at this time.
Add slack variables, can the training error of SVM be 0?
In practice, the SMO algorithm is used to train a linear SVM model with slack variables, and the penalty factor is any unknown constant, and a model with a training error of 0 may not be obtained.
The objective function of the SVM model with slack variables contains these two items: 
when C=0, =0, the optimization goal is reached, and the training error is not necessarily zero at this time.