I am confused about the general rule of Lagrangian multiplier. (which usully use for SVM). I could not find a good book or paper that explain it completely and clearly.
Suppose we have
$$minimize: w^{2}$$
Subject to $$f(x) \leq 0$$
Lagragian multiplier say we can solve the following
$$min : \; \; w^{2}+\lambda f(x) $$
subject to $$ \lambda \geq 0$$
Then we solve gradian equations and substitute back in Lagrangian.
1- how we make sure the solution satisfy f(x) <0 ?
2- what is extra constraints in dual representation?
