|
In mathematics, a global optimum is a selection from a given domain which provides either the highest value (the global maximum) or lowest value (the global minimum), depending on the objective, when a specific function is applied. For example, for the function :''f''(''x'') = −''x''2 + 2, defined on the real numbers, the global maximum occurs at ''x'' = 0, where ''f''(''x'') = 2. For all other values of ''x'', ''f''(''x'') is smaller. For purposes of optimization, a function must be defined over the whole domain, and must have a range which is a totally ordered set, in order that the evaluations of distinct domain elements are comparable. By contrast, a local optimum is a selection for which ''neighboring'' selections yield values that are not greater (for a local maximum) or not smaller (for a local minimum). The concept of a local optimum implies that the domain is a metric space or topological space, in order that the notion of "neighborhood" should be meaningful. If the function to be maximized is quasi-concave, or if the function to be minimized is quasi-convex, then a local optimum is also the global optimum. ==See also== *Maxima and minima 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「global optimum」の詳細全文を読む スポンサード リンク
|