发表机构
Karlsruhe Institute of Technology; University of Southampton（卡尔斯鲁厄理工学院; 南安普顿大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一种不依赖互补条件或最优值函数的真正单层重构（tSLR），使悲观双层优化满足经典约束规范，构建新最优性条件，实验表明其算法优于现有方法，表明该类问题可能更易求解。
AI 中文摘要
我们针对悲观双层优化问题提出了一种不依赖于互补条件或最优值函数的单层重构（SLR）。因此，我们将其称为真正的单层重构（tSLR）。一个显著的结果是，这种重构能够满足经典的线性无关约束规范，尽管已知即使是较弱的Mangasarian-Fromovitz约束规范在乐观和悲观双层规划的标准单层重构中也会系统性地失效。我们利用这些约束规范为悲观双层优化构建了新的必要最优性条件。该重构也有一个显著的局限性：在我们分析的假设下，经典的二阶充分条件在问题的每个Karush-Kuhn-Tucker点处均不成立。尽管如此，初步数值实验表明，基于所提出的tSLR的算法在悲观双层优化中可以优于现有方法。总体而言，所提出的框架表明，悲观双层规划可能比以前认为的更容易处理，并且不一定比其乐观对应问题更难求解。
英文摘要
We propose a single-level reformulation (SLR) for the pessimistic bilevel optimization problem that does not rely on complementarity conditions or optimal value functions. For this reason, we refer to it as a true single-level reformulation (tSLR). A remarkable consequence is that this reformulation can satisfy the classical linear independence constraint qualification, despite the fact that even the weaker Mangasarian-Fromovitz constraint qualification is known to systematically fail for standard single-level reformulations of both optimistic and pessimistic bilevel programs. We leverage on these constraint qualifications to construct new necessary optimality conditions for pessimistic bilevel optimization. The reformulation also has a striking limitation: under the assumptions of our analysis, the classical second-order sufficient condition fails at every Karush-Kuhn-Tucker point of the problem. Nevertheless, preliminary numerical experiments demonstrate that algorithms based on the proposed tSLR can outperform existing approaches for pessimistic bilevel optimization. Overall, the proposed framework suggests that pessimistic bilevel programs may be considerably more tractable than previously believed and need not be inherently more difficult to solve than their optimistic counterparts.
Comments33 pages, 7 figures
