Conic dual problem
= Conic dual problem
For $\min_x c^\top x$ subject to $Ax-b\in K$, the <Lagrangian dual problem> is $\max_y b^\top y$ subject to $A^\top y=c$ and $y\in K^*$. At feasible primal-dual points, the gap is $\langle Ax-b,y\rangle\geq0$. A self-dual cone has $K^*=K$, but self-duality alone does not imply feasibility or <strong duality>.