(abbrev. min), n. 1. the least element of a set, usually denoted minS. For example, the positive numbers have no minimum, but the non-negative numbers have minimum 0, although both have 0 as infimum. See minimal. 2. the lowest value of a function, usually denoted min f; it is a global minimum if this condition is satisfied with respect to all other values of the function. A local minimum is a value less than any other in a neighborhood of its argument, and is identified in the real differentiable setting by having zero first derivative and positive second derivative since the tangent to the curve changes from falling to rising at this point. In the figure below, the left-hand minimum is global, and the other is local. See first and second derivative tests. A graph with a global minimum at A and a local minimum at B.