Stochastic absolute value equations
Abstract
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.
Cite
@article{arxiv.2207.05918,
title = {Stochastic absolute value equations},
author = {Shouqiang Du and Jingjing Sun and Shengqun Niu and Liping Zhang},
journal= {arXiv preprint arXiv:2207.05918},
year = {2022}
}