Linear complementarity problem: Difference between revisions

Revision as of 18:25, 19 May 2010

Revision as of 18:53, 4 June 2010

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If '''M''' is [[Positive-definite matrix|positive definite]], any algorithm for solving (convex) [[Quadratic programming|QPs]] can of course be used to solve the LCP. However, there also exist more efficient, specialized algorithms, such as [[Lemke's algorithm]] and [[Simplex algorithm | Dantzig's algorithm]].

Also, a quadratic programming problem stated as minimize <math>f(\mathbf{x})=\mathbf{c}^T\mathbf{x}+\frac{1}{2}\mathbf{x}^T\mathbf{Qx}</math> subject to <math>\mathbf{Ax} \geq 0\mathbf{b}</math>

is the same as solving the LCP with