I am going to code from scratch for Soft-margin Kernelised SVM, therefore, I am going to solve the dual form such as to kernelised.
Since most of the Penalty Method and Augmented Lagrangian Method examples are for equality constraints. I know that there are some extension for these methods so as to solve inequality constraints. However, I am not sure whether these extension is stable for solving soft-margin kernelised SVM's dual form.
Is there any case that the extension of solving inequality constraints via Penalty or Augmented Lagrangian will be unstable and some techniques to deal with it? as there are not many materials about this extension.
Thank you very much
What about to use the penalty method for equality constrains and the barrier method for inequality constrains (https://en.wikipedia.org/wiki/Barrier_function)? This is quite usual and numerically effective approach.