It is possible to solve any 2D problems (or two constraints for a dual problem) by a graph.
We obtain the global optimal solution. If we draw again the objective function following the gradient, the line will be outside the definition domain.
There are four possibilities:
- an unique solution exists (one point);
- an infinity of solutions (a facet);
- the solution is not bounded, the line of the objective function will always be in the definition domain following the gradient;
- or there is no solution, for example if the domain is empty.