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通过简单函数确定多变量分布稳定约束的正半确定安全近似

Jana Dienstbier¹, Frauke Liers¹, Jan Rolfes^2,1

¹Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstr. 11, 91058 Erlangen, Germany.

Journal of optimization theory and applications

|September 5, 2025

概括

这项研究引入了对非凸函数的难以处理的分布强度优化 (DRO) 问题的安全近似. 该方法可以计算复杂的DRO模型的可证明可靠的解决方案.

科学领域:

优化情况
运营研究
机器学习

背景情况:

由于半无限的双重约束,非凸度的分布强度优化 (DRO) 问题往往是计算难以解决的.
现有的方法通常需要强有力的假设,如凸度或度,限制了它们的适用性.
之前的研究涉及单变量函数,而多变量函数则基本未被研究.

研究的目的:

开发一个安全的近似对非凸分布强度优化 (DRO) 问题的单级重构.
扩展现有方法以处理多变量简单的DRO函数.
为更广泛的DRO问题提供可行和可证明的可靠解决方案.

主要方法:

利用基于二元性的重制方法来解决具有简单函数的DRO问题.
将方法从单变量扩展到多变量不确定性参数.
通过离散对应对半无限双约束实现安全近似.
将问题构成一个可计算的混合整数正半定义程序.

主要成果:

为非凸多变量DRO问题提出了一个新的安全近似值.
接近允许将瞬间信息和信任集纳入模两可的集合.
该方法产生了一个可处理的混合整数正半定义程序,可以用现有的软件解决.
接近提供了足够的分布稳定性条件,确保可证明的稳定性解决方案.

结论:

拟议的安全近似显著扩大了DRO重构的适用性,用于非凸的多变量问题.
算法可操作性是通过离散实现的,使得可靠解决方案的实际计算成为可能.
该方法为解决复杂的DRO实例提供了计算效率高且理论上合理的方法.

关键词:

在分布上强大的优化混合整数优化强大的优化随机优化

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