Some remarks about a multifunction approach to geodesic-type problems via image space analysis

The paper contains a proposal for visiting again the geodesic-type problems in the light of Image Space Analysis. By means of a multifunction approach it is possible to associate a finite dimensional image to the given problem and to provide an interpretation, in terms of a selection, of the classic Euler-Lagrange multipliers, which is also illustrated with the help of a simple numerical example.