In this work, we show the consistency of an approach for solving robust optimization problems using sequences of sub-problems generated by ergodic measure preserving transformations. The main result of this paper is that the minimizers and the optimal value of the sub-problems converge, in some sense, to the minimizers and the optimal value of the initial problem, respectively. Our result particularly implies the consistency of the scenario approach for nonconvex optimization problems. Finally, we show that our method can also be used to solve infinite programming problems.

中文翻译：

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鲁棒优化和无限编程问题的遍历方法

在这项工作中，我们展示了使用遍历测度保留转换生成的子问题序列来解决鲁棒优化问题的方法的一致性。本文的主要结果是，在某种意义上，子问题的极小值和最优值分别收敛于初始问题的极小值和最优值。我们的结果特别暗示了针对非凸优化问题的方案方法的一致性。最后，我们证明了我们的方法也可以用于解决无限编程问题。