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Given a system transforming a set of inputs to output values, described by a mathematical function ''f'', optimization refers to the generation and selection of a best solution from some set of available alternatives,〔"(The Nature of Mathematical Programming )," ''Mathematical Programming Glossary'', INFORMS Computing Society.〕 by systematically choosing input values from within an allowed set, computing the value of the function, and recording the best value found during the process. Many real-world and theoretical problems may be modeled in this general framework. For example, the inputs can be design parameters of a motor, the output can be the power consumption, or the inputs can be business choices and the output can be the obtained profit, or the inputs can describe the configuration of a physical system and the output can be its energy. An optimization problem can be represented in the following way :''Given:'' a function ''f'' : ''A'' R from some set ''A'' to the real numbers :''Search for:'' an element ''x''0 in ''A'' such that ''f''(''x''0) ≤ ''f''(''x'') for all ''x'' in ''A'' ("minimization"). Typically, ''A'' is some subset of the Euclidean space R''n'', often specified by a set of ''constraints'', equalities or inequalities that the members of ''A'' have to satisfy. Maximization can be reduced to minimization by multiplying the function by minus one. The use of optimization software requires that the function ''f'' is defined in a suitable programming language and linked to the optimization software. The optimization software will deliver input values in ''A'', the software module realizing ''f'' will deliver the computed value ''f''(''x''). In this manner, a clear separation of concerns is obtained: different optimization software modules can be easily tested on the same function ''f'', or a given optimization software can be used for different functions ''f''. The following tables provide a comparison of optimization software libraries, either specialized or general purpose libraries with significant optimization coverage. ==References== 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「Comparison of optimization software」の詳細全文を読む スポンサード リンク
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