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.

Keywords:

• stochastic linear complementarity problem
• expected residual minimization
• Barzilai–Borwein method
• nonmonotone line search
• nonsmooth

2010 AMS Subject Classifications:

• 65K10
• 90C26

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

This work was supported by the National Natural Science Foundation of China (NNSFC) under Grant No. 61072144 and No. 61179040 and the Fundamental Research Funds for the Central Universities No. K50513100007 and JB142001-4.