Linear complementarity problem
Linear complementarity problem From Wikipedia, the free encyclopedia 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 in 1968. [1] [2] [3] Contents [ hide ] 1 Formulation 2 Convex quadratic-minimization: Minimum conditions 3 See also 4 Notes 5 References 6 Further reading 7 External links Formulation [ edit ] 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: {\displaystyle w,z\geqslant 0,} (that is, each component of these two vectors is non-negative) {\displaystyle z^{T}w=0} or equivalently {\displaystyle \sum \nolimits _{i}w_{i}z_{i}...