Convergence proof of PGS for box constrained MLCP

[BenMeijering]

Hi,

Theorem 9.7 to Corollary 9.3 in Murty's "Linear Complementarity,
Linear and Nonlinear Programming" give proof for the convergence of (amongst others) PGS in the case that M is symmetric PD.

But it is only proven for a LCP in this form:

w = Mz + q
w,z >= 0
w_transp * z = 0

Does anyone have any references or information on how these proofs can be modified or extended to prove the convergence of the solver in Erleben's "Physics Based Animation" (corollary 19.1) to solve the following box constrained MLCP in the case that M is symmetric PD:

w = Mz + q
li <= zi <= hi
zi = li -> wi >= 0
li < zi < hi -> wi = 0
zi = hi -> wi <= 0

(note: l and h are fixed)

Thanks in advance for your help.

Regards,

Ben