Distributionally robust expected residual minimization for stochastic variational inequality problems
Distributionally robust expected residual minimization for stochastic variational inequality problems
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DOI：
10.1080/10556788.2023.2167995
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发表时间：
2021-11
影响因子：
2.2
通讯作者：
A. Hori;Yuya Yamakawa;N. Yamashita
中科院分区：
文献类型：
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作者：
A. Hori;Yuya Yamakawa;N. Yamashita
随机变异不平等问题（SVIP）是一个均衡模型，包括随机变量，已广泛应用于经济学和工程等各个领域。预期残留最小化（ERM）是为SVIP获取合理解决方案的既定模型，其目标函数是SVIP合适的优点函数的期望值。但是，ERM仅限于提前已知分布的情况。我们扩展了ERM，以确保在不确定性分布下实现SVIP的可靠溶液（扩展的ERM被称为分布在分布上具有强大的预期残留最小化（DRERM），其中最坏情况下的分布来自最差的案例分布。预期值和方差分别采用相同的样本均值和方差）。在适当的假设下，我们证明了DRER可以作为确定性凸的非线性半决赛编程进行重新重新制定，以避免数值集成。
The stochastic variational inequality problem (SVIP) is an equilibrium model that includes random variables and has been widely applied in various fields such as economics and engineering. Expected residual minimization (ERM) is an established model for obtaining a reasonable solution for the SVIP, and its objective function is an expected value of a suitable merit function for the SVIP. However, the ERM is restricted to the case where the distribution is known in advance. We extend the ERM to ensure the attainment of robust solutions for the SVIP under the uncertainty distribution (the extended ERM is referred to as distributionally robust expected residual minimization (DRERM), where the worst-case distribution is derived from the set of probability measures in which the expected value and variance take the same sample mean and variance, respectively). Under suitable assumptions, we demonstrate that the DRERM can be reformulated as a deterministic convex nonlinear semidefinite programming to avoid numerical integration.