Lagrangian dual problem

For a minimization problem with inequalities $g_i(x)\le 0$, the Lagrangian is $L(x,\lambda )=f(x)+{\sum }_i{\lambda }_i{g}_i(x)$ with ${\lambda }_i\ge 0$. The Lagrangian dual maximizes the concave dual function $q(\lambda )={\inf }_{x}L(x,\lambda )$.