| 单词 | constrained maximum |
| 释义 | constrained maximum The maximum possible value for a function, consistent with satisfying one or more inequalities. For example, a consumer seeks to maximize utility subject to a budget constraint, that is, a limit on the amount he or she can spend. In this case, if wants are assumed insatiable, the budget constraint is always effective, but in other problems constraints may not be effective. There may be any number of constraints, each of which may or may not be effective. For example, consider the problem of maximizing U = f(x, y) subject to g(x, y) ≤ 0. If it is known that the constraint is not effective, it can be disregarded. If it is known that it is effective, that is that g(x, y) = 0, then it may be possible to use the constraint to express x in terms of y, turning U into a function of y only, which is then maximized in the normal way. In cases where it is not known whether the constraint is effective, a Lagrange multiplier is frequently used. The original problem is replaced by that of finding a stationary value of L = f(x, y) + λg(x, y). The three equations ∂L/∂x = 0, ∂L/∂y = 0 and g(x, y) = 0 are used to determine x, y and λ. This gives the x and y which maximize U subject to the constraint; if λ > 0 the constraint is effective. |
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