We consider the stochastic linear complementarity
problem (SLCP) involving a random matrix whose expectation matrix
is positive semi-definite. We show that the expected
residual minimization (ERM) formulation of this problem
has a nonempty and bounded solution set if
the expected value (EV) formulation, which reduces to the LCP with
the positive semi-definite expectation matrix, has a nonempty and
bounded solution set. Moreover, by way of a regularization technique,
we prove that the solvability of the EV formulation implies
the solvability of the ERM formulation.
We give a new error bound for the monotone LCP and use it to show
that solutions of the ERM formulation are robust in the sense
that they may have a minimum sensitivity with respect to random
parameter variations in SLCP.
Numerical results are given to illustrate the characteristics of the
solutions.