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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: * * (that is, each component of these two vectors is non-negative) * (The complementarity condition). This can also be written as . 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 is a slack variable,〔.〕 and so is generally discarded after is found. As such, the problem can also be formulated as: * * * (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
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