Numer Algor (2011) 58:593–618 DOI 10.1007/s11075-011-9472-7 ORIGINAL PAPER Partial projected Newton method for a class of stochastic linear complementarity problems Hongwei Liu · Yakui Huang · Xiangli Li Received: 13 November 2010 / Accepted: 15 May 2011 / Published online: 23 June 2011 © Springer Science+Business Media, LLC 2011 Abstract This paper considers a class of stochastic linear complementarity problems (SLCPs) with finitely many realizations. We first formulate this class of SLCPs as a minimization problem. Then, a partial projected Newton method, which yields a stationary point of the minimization problem, is pre- sented. The global and quadratic convergence of the proposed method is proved under certain assumptions. Preliminary experiments show that the algorithm is efficient and the formulation may yield a solution with various desirable properties. Keywords Partial projected Newton method · Stochastic linear complementarity problems Mathematics Subject Classifications (2010) 90C30 · 90C33 1 Introduction Let (, F , P ) be a probability space with  ⊆ R l . Suppose the probabil- ity distribution P is known. The stochastic linear complementarity problem (SLCP) [2, 3, 8, 12, 13, 18] is to find an x ∈ R n such that x ≥ 0, M(ω)x + q(ω) ≥ 0, x T ( M(ω)x + q(ω)) = 0,ω ∈ , (1) This project was supported by the National Natural Science Foundation of China (Grant No. 61072144). H. Liu · Y. Huang (B ) · X. Li Department of Mathematics, Xidian University, Xi’an 710071, People’s Republic of China e-mail: huangyakui2006@gmail.com