Linear complementarity problem: Difference between revisions

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In mathematical [[optimization (mathematics)|optimization theory]], the '''linear complementarity problem''', or '''LCP''', is a special case of [[quadratic programming]] which arises frequently in [[computational mechanics]]. Given a real matrix '''M''' and vector '''b''', the linear complementarity problem seeks a vector '''x''' which satisfies the following two constraints:

* <math>\mathbf{Mx}+\mathbf{b} >\ge \mathbf{0}</math> and <math>\mathbf{x} >\ge \mathbf{0}</math>; that is, each component of these two vectors is positivenon-negative, and

* <math>\mathbf{x}^{\mathrm{T}}(\mathbf{Mx}+\mathbf{b}) = 0</math>, the '''complementarity condition'''.