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.