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In mathematical optimization, the method of Lagrange multipliers (named after Joseph Louis Lagrange) provides a strategy for finding the local maxima and minima of a function (mathematics)|function subject to constraint (mathematics)|equality constraints. For instance (see Figure 1), consider the optimization problem :maximize f(x, y) \, :subject to g(x, y) = c.\,We need both f and g to have continuous first partial derivatives. We introduce a new variable (\lambda) called a Lagrange multiplier and study the Lagrange function defined by : \Lambda(x,y,\lambda) = f(x,y) + \lambda \cdot \Big(g(x,y)-c\Big), where the \lambda term may be either added or subtracted. If f(x_0, y_0) is a maximum of f(x,y) for the original constrained problem, then there exists \lambda_0 such that (x_0,y_0,\lambda_0) is a stationary point for the Lagrange function (stationary points are those points where the partial derivatives of \Lambda are zero, i.e. \nabla\Lambda = 0). However, not all stationary points...
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