Lagrange Multipliers on Banach Spaces
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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 ...
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.
