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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク integer programming ： ウィキペディア英語版 integer programming An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers. In many settings the term refers to integer linear programming (ILP), in which the objective function and the constraints (other than the integer constraints) are linear. Integer programming is NP-hard. A special case, 0-1 integer linear programming, in which unknowns are binary, and only the restrictions must be satisfied, is one of Karp's 21 NP-complete problems. ==Canonical and standard form for ILPs== An integer linear program in canonical form is expressed as: :$\backslash begin$ & \text && \mathbf^\mathrm \mathbf\\ & \text && A \mathbf \le \mathbf, \\ & && \mathbf \ge \mathbf, \\ & \text && \mathbf \in \mathbb^n, \end , and an ILP in standard form is expressed as :$\backslash begin$ & \text && \mathbf^\mathrm \mathbf\\ & \text && A \mathbf + \mathbf = \mathbf, \\ & && \mathbf \ge \mathbf, \\ & \text && \mathbf \in \mathbb^n, \end where the entries of $\backslash mathbf,\; \backslash mathbf$ are vectors and $A$ is a matrix, having integer values. Note that similar to linear programs, ILPs not in standard form can be converted to standard form by eliminating inequalities by introducing slack variables ($\backslash mathbf$) and replacing variables that are not sign-constrained with the difference of two sign-constrained variables 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「integer programming」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.