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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 Lagrangian relaxation ： ウィキペディア英語版 Lagrangian relaxation In the field of mathematical optimization, Lagrangian relaxation is a relaxation method which approximates a difficult problem of constrained optimization by a simpler problem. A solution to the relaxed problem is an approximate solution to the original problem, and provides useful information. The method penalizes violations of inequality constraints using a Lagrange multiplier, which imposes a cost on violations. These added costs are used instead of the strict inequality constraints in the optimization. In practice, this relaxed problem can often be solved more easily than the original problem. The problem of maximizing the Lagrangian function of the dual variables (the Lagrangian multipliers) is the Lagrangian dual problem. ==Mathematical description== Given a linear programming problem $x\backslash in\; \backslash mathbb^n$ and $A\backslash in\; \backslash mathbb^$ of the following form: : If we split the constraints in $A$ such that $A\_1\backslash in\; \backslash mathbb^$, $A\_2\backslash in\; \backslash mathbb^$ and $m\_1+m\_2=m$ we may write the system: : We may introduce the constraint (2) into the objective: : If we let $\backslash lambda=(\backslash lambda\_1,\backslash ldots,\backslash lambda\_)$ be nonnegative weights, we get penalized if we violate the constraint (2), and we are also rewarded if we satisfy the constraint strictly. The above system is called the Lagrangian Relaxation of our original problem. 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「Lagrangian relaxation」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.