A new formulation for a class of stochastic linear complementarity problems (SLCPs) with finitely many realizations is proposed, which reformulates the SLCPs as a system of smoothing equations without any constraints by an NCP function. Then, we extend an one step smoothing Newton method to this formulation. Moreover, we show that this algorithm converges globally and local quadratically under mild assumptions.
"An One Step Smoothing Newton Method for a Class of Stochastic Linear Complementarity Problems." Bull. Belg. Math. Soc. Simon Stevin 18 (2) 337 - 344, may 2011. https://doi.org/10.36045/bbms/1307452083