论文标题
随机绝对价值方程
Stochastic absolute value equations
论文作者
论文摘要
我们提出了一种涉及变量绝对值的新型随机绝对值方程。通过利用与随机双线性程序的等价关系，我们研究了所提出的随机绝对值方程的期望值公式。我们还考虑了所提出的随机绝对值方程的预期残留最小化公式。在温和的假设下，我们给出了解决随机绝对值方程的解决条件。随机绝对值方程的解可以通过解决离散最小化问题来获得。我们还提出了一种平滑梯度方法来解决离散最小化问题。最后，给出了数值结果和一些讨论。
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.
