| 单词 | minimum |
| 释义 | minimum The lowest value a function takes for any value of its arguments. A minimum may be local or global. For example, y = 1 + x2 has a global minimum of y = 1 when x = 0; there is no value of x which gives a lower y. It is a necessary condition for a local minimum of a function y = f(x) that dy/dx = 0; given that dy/dx = 0, it is a sufficient but not a necessary condition for a local minimum that d2 y/dx2 > 0. Consider, however, the function z = x3 - 3x. This has a minimum z = -2 at x = 1, but this is only a local minimum, that is, z is lower for x = 1 than for nearby values of x. Sufficiently large negative values of x can make z lower without limit, so that z does not have a global minimum. The minimum of a set of xi, i = 1, 2,…, N, or arg min [x1, x2,…, xN ] is the smallest value of any xi. See also: maximum, constrained minimum, global minimum, and local minimum |
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