Ms. Gowda et R. Sznajder, THE GENERALIZED ORDER LINEAR COMPLEMENTARITY-PROBLEM, SIAM journal on matrix analysis and applications, 15(3), 1994, pp. 779-795
The generalized order linear complementarity problem (in the setting o
f a finite dimensional vector lattice) is the problem of finding a sol
ution to the piecewise-linear system x AND (M1x + q1 ) AND (M2x + q2)
AND ... AND (M(k)x + q(k)) = 0, where M(i)'s are linear transformation
s and q(i)'s are vectors. This problem is equivalent to the generalize
d linear complementarity problem considered by Cottle and Dantzig [J.
Combin. Theory, 8 (1970), pp- 79-90.]. Using degree theory, a comprehe
nsive analysis of existence, uniqueness, and stability aspects of this
problem is presented.