Stochastic absolute value equations

We propose a new kind of stochastic absolute value equations involving absolute values of variables. By utilizing an equivalence relation to stochastic bilinear program, we investigate the expected value formulation for the proposed stochastic absolute value equations. We also consider the expected residual minimization formulation for the proposed stochastic absolute value equations. Under mild assumptions, we give the existence conditions for the solution of the stochastic absolute value equations. The solution of the stochastic absolute value equations can be gotten by solving the discrete minimization problem. And we also propose a smoothing gradient method to solve the discrete minimization problem. Finally, the numerical results and some discussions are given.

Automated summary

In this paper, a new type of stochastic absolute value equations involving absolute values of variables is proposed. By utilizing an equivalence relation and expected value formulation, the solution conditions for the equations are given. The discrete minimization problem is solved by a smoothing gradient method. Numerical results and discussions are presented.