Lagrange multiplier

Figure 1: Find x and y to maximize f(x, y) subject to a constraint (shown in red) g(x, y) = c.

Figure 2: Contour map of Figure 1. The red line shows the constraint g(x, y) = c. The blue lines are contours of f(x, y). The point where the red line tangentially touches a blue contour is the solution. Since d1 > d2, the solution is a maximization of f(x, y).

Figure 3: A paraboloid constrained along two intersecting lines.

In mathematical optimization, the method of Lagrange multipliers (named after Joseph Louis Lagrange) is a strategy for finding the local maxima and minima of a function subject to equality constraints.

For instance (see Figure 1), consider the optimization problem

单词	Lagrange multipliers
释义	Lagrange multipliers 英语百科 Lagrange multiplier In mathematical optimization, the method of Lagrange multipliers (named after Joseph Louis Lagrange) is a strategy for finding the local maxima and minima of a function subject to equality constraints. For instance (see Figure 1), consider the optimization problem
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