| 单词 | Lagrange multiplier |
| 释义 | Lagrange multiplier A notional variable introduced to help in finding constrained maximum and minima. Suppose that a function y = f(x, z) has to be maximized subject to the constraint that g(x, z) ≤ k. One approach to this problem is to locate a stationary value of the expression L = f(x, z) - λ[g(x, z) - k]. Where fx denotes ∂f(x, z)/∂x, etc, L takes a stationary value where Lx = Lz = 0; but Lx = fx - λgx and Lz = fz - λgz. If the constraint is not binding, λ = 0 and y is maximized where fx = fy = 0. If the constraint is binding, λ > 0 and a stationary value of y exists at the values of x and z found by solving the three equations Lx = 0, Ly = 0 and g(x, z) = k. L is the Lagrangean expression, and λ is the Lagrange multiplier. λ can be regarded as a shadow prices, giving the effect on y of an increase in k. For example, y could be utility, which is maximized subject to the constraint that total spending on x and z is less than or equal to income, k. |
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