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global optimization : ウィキペディア英語版
global optimization

Global optimization is a branch of applied mathematics and numerical analysis that deals with the global optimization of a function or a set of functions according to some criteria. Typically, a set of bound and more general constraints is also present, and the decision variables are optimized considering also the constraints.
Global optimization is distinguished from regular optimization by its focus on finding the maximum or minimum over all input values, as opposed to finding ''local'' minima or maxima.
== General ==

A common (standard) model form is the minimization of one real-valued function
f in the parameter-space \vec\in P, or its specified subset \vec\in D: here D denotes the set defined by the constraints.
(The maximization of a real-valued function g(x) is equivalent to the minimization of the function f(x):=(-1)\cdot g(x).)
In many nonlinear optimization problems, the objective function f has a large number of ''local'' minima and maxima. Finding an arbitrary local optimum is relatively straightforward by using classical ''local optimization'' methods. Finding the global minimum (or maximum) of a function is far more difficult: symbolic (analytical) methods are frequently not applicable, and the use of numerical solution strategies often leads to very hard challenges.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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