Primal problem and dual problem

The original question

The dual problem

The relation between primal problem and dual problem

Distance between primal problem and dual problem G：

For some specific optimization problems , Can prove that G=0.

Strong duality theorem

if f(w) Is a convex function , And g(w)=Aw+b,h(w)=cw+d. Then the distance between the primal problem and the dual problem of this optimization problem is 0.

We call this condition KKT Conditions .