The Lagrange multipliers method is used in Mathematical Analysis, in Mechanics, in Economics and in several other fields, to deal with the search of the global maximum or minimum of a function, in presence of a constraint. The usual technique, applied to the case of finite-dimensional systems, transforms the constrained optimization problem into an unconstrained one, by means of the introduction of one or more multipliers and of a suitable Lagrangian function, to be optimized. In Mechanics, several optimization problems can be applied to infinite-dimensional systems. Lagrange multipliers method can be applied also to these cases.