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High Quality Content by WIKIPEDIA articles! In the field of calculus of variations in mathematics, the method of Lagrange multipliers on Banach spaces can be used to solve certain infinite-dimensional constrained optimization problems. The method is a generalization of the classical method of Lagrange multipliers as used to find extrema of a function of finitely many variables.Let X and Y be real Banach spaces. Let U be an open subset of X and let f : U R be a continuously differentiable function. Let g : U Y be another continuously differentiable function, the constraint: the objective is to find the extremal points (maxima or minima) of f subject to the constraint that g is zero.