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optimization problem : ウィキペディア英語版
optimization problem
In mathematics and computer science, an optimization problem is the problem of finding the ''best'' solution from all feasible solutions. Optimization problems can be divided into two categories depending on whether the variables are continuous or discrete. An optimization problem with discrete variables is known as a combinatorial optimization problem. In a combinatorial optimization problem, we are looking for an object such as an integer, permutation or graph from a finite (or possibly countable infinite) set. Problems with continuous variables include constrained problems and multimodal problems.
==Continuous optimization problem==
The ''standard form'' of a (continuous) optimization problem is
: \begin
&\underset
& &g_i(x) \leq 0, \quad i = 1,\dots,m \\
&&&h_i(x) = 0, \quad i = 1, \dots,p
\end
where
* f(x): \mathbb^n \to \mathbb is the objective function to be minimized over the variable x,
* g_i(x) \leq 0 are called inequality constraints, and
* h_i(x) = 0 are called equality constraints.
By convention, the standard form defines a minimization problem. A maximization problem can be treated by negating the objective function.

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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