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For Linear complementarity problems (LCP) like

  • $\mathbf{Mz}+\mathbf{q} \ge \mathbf{0}$
  • $\mathbf{z} \ge \mathbf{0}$
  • $\mathbf{z}^{\mathrm{T}}(\mathbf{Mz}+\mathbf{q}) = 0$

there exists a vast amount of material and algorithms. But what about this kind of problem:

  • $\mathbf{Mz}+\mathbf{q} \ge \mathbf{0}$
  • $\mathbf{Az} +\mathbf{b}\ge \mathbf{0}$
  • $(\mathbf{Az} +\mathbf{b})^{\mathrm{T}}(\mathbf{Mz}+\mathbf{q}) = 0$

Is it also called LCP? Can it be transformed into the form above?

The real question is, how to solve it without the need to invert on of the matrices explicitly.

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  • $\begingroup$ Don't post to two different places simultaneously: math.stackexchange.com/questions/26541. Voting to close here. $\endgroup$ Mar 12, 2011 at 11:44
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    $\begingroup$ why not? why does the appearance of a question in one forum prohibit its appearance in another forum? $\endgroup$
    – Johannes
    Mar 12, 2011 at 14:37
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    $\begingroup$ @Johannes: See tea.mathoverflow.net/discussion/943. Basically, it's simply impolite to simultaneously post a question to different forums, especially if you don't give any indication that you have done so. $\endgroup$ Mar 12, 2011 at 19:45

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