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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 Linear complementarity problem ： ウィキペディア英語版 Linear complementarity problem In mathematical optimization theory, the linear complementarity problem (LCP) arises frequently in computational mechanics and encompasses the well-known quadratic programming as a special case. It was proposed by Cottle and Dantzig == Formulation == Given a real matrix M and vector q, the linear complementarity problem LCP(M,q) seeks vectors z and w which satisfy the following constraints: * $=\; +\; \backslash ,$ * $\backslash ge\; 0,\; \backslash ge\; 0\backslash ,$ (that is, each component of these two vectors is non-negative) * $\backslash Sigma\_i\_i\; \_i\; =\; 0\backslash ,$ (The complementarity condition). This can also be written as $z^Tw\; =\; 0$. A sufficient condition for existence and uniqueness of a solution to this problem is that M be symmetric positive-definite. If M is such that LCP(M,q) have a solution for every q, then M is a Q-matrix. If M is such that LCP(M,q) have a unique solution for every q, then M is a P-matrix. Both of these characterizations are sufficient and necessary. The vector $\backslash ,$ is a slack variable,〔.〕 and so is generally discarded after $\backslash ,$ is found. As such, the problem can also be formulated as: * $+\; \backslash ge\; \backslash ,$ * $\backslash ge\; \backslash ,$ * $^+)\; =\; 0\backslash ,$ (the complementarity condition) 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「Linear complementarity problem」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.