| 单词 | constrained minimum |
| 释义 | constrained minimum The minimum possible value for a function, consistent with satisfying one or more inequalities. For example, a firm seeks to minimize the costs of producing a given output. In this case the 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 minimizing C = f(x,y) subject to g(x, y) ≥ 0, where x and y are inputs. 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 C into a function of y only, which is then minimized 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 minimize C subject to the constraint; if λ > 0 the constraint is effective. |
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