To confirm: The sign of the dual variable on a constraint of `JuMP` model

Hi, Prof. @odow , I have another question about duality but I don’t know if it is appropriate to ask here.

The question is: To solve a convex primal problem PP I first derive its dual problem DP and then I model and solve the dual problem DP using JuMP. Now after I obtain the optimal solution of the dual problem DP, how can I retrieve the primal solution of some of the primal variables?

I guess maybe the optimal solution of some primal variables correspond to the dual value of some constraints in DP, but how can I tell what the correspondence is between them?

Suppose the KKT conditions are, if they help:

\begin{eqnarray} f_i(x)\leqslant 0,&\quad i = 1,\cdots,m\\ h_i(x) = 0,&\quad i = 1,\cdots,p~~\\ {\lambda}_i\geqslant 0,&\quad i = 1,\cdots,m\\ {\lambda}_i f_i({x}) = 0,&\quad i = 1,\cdots,m\\ \nabla f_0({x}) + \sum_{i=1}^m{\lambda}_i\nabla f_i({x}) + \sum_{i=1}^p{\nu}_i\nabla h_i({x}) = 0.&\\ \end{eqnarray}