LINEAR COMPLEMENTARITY PROBLEMS WITH UNCERTAIN VARIABLES

Under the uncertainty theory, the uncertain linear complementarity problem(ULCP) with uncertain variables is proposed. Firstly, uncertain expected residual minimization model(UERM) is established. Secondly, we study the boundedness of the level set of the UERM problem. The Stieltjes integral method is used to discretize the expectation of uncertain variables, and results show that each minimum accumulation point of the discrete approximation problem is the minimum expected residual solution of the ULCP. Finally, the existence and convergence of solutions for ULCP are proved.