2D graphical resolution

It is possible to solve any 2D problems (or two constraints for a dual problem) by a graph.

We represent each constraint in the graph, hatching or coloring the side that does not satisfy the constraint.
We highlight a domain, any point of this domain satisfies all the constraints of the mathematical model.

graphique

In order to solve the problem, we represent the objective function at the point (0,0) and then at various points (following the gradient of the objective function) until the objective function has only one point or one facet of the domain.

We obtain the global optimal solution. If we draw again the objective function following the gradient, the line will be outside the definition domain.

graphique2

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.

 

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