Smoothing projected cyclic Barzilai–Borwein method for stochastic linear complementarity problems

Abstract

In this paper, we propose a smoothing projected cyclic Barzilai–Borwein (SPCBB) method for solving the expected residual minimization formulation of stochastic linear complementarity problems (SLCPs). The SPCBB method combines the smoothing techniques and the projected Barzilai–Borwein (BB) method, where the cyclic BB scheme which resues the same BB stepsize for several consecutive iterations and a nonmonotone line search that requires an average of the successive function values decreases are employed to accelerate the convergence process. Under mild conditions, we show the convergence of the proposed method to a Clarke stationary point. Preliminary numerical results of randomly generated SLCPs show that the method is promising.