Eghbal Hosseini · 2026 · arXiv
DOI: 10.48550/arXiv.2610.27909 · open-access PDF
最糟糕的案例显示了优化算法失败的地方:简单方法的Klee-Minty立方体,降级降落的条件不佳和裂缝的碗,牛顿方法的降级最低限度,内部点方法的剩余Klee-Minty立方体,分支和束缚的不可磨灭的树木,甲骨文学的欺骗性景观,以及活跃组方法的退化自行车。这些构造在独立文献中发展了70多年,每个都有自己的工具。
Machine translation (Meta M2M100); the English original follows.
Worst-case instances show where optimization algorithms fail: the Klee-Minty cube for the simplex method, ill-conditioned and rippled bowls for gradient descent, degenerate minima for Newton's method, redundant Klee-Minty cubes for interior-point methods, unprunable trees for branch-and-bound, deceptive landscapes for metaheuristics, and degenerate cycling for active-set methods. These constructions were developed over seventy years in separate literatures, each with its own tools. This survey reviews them together. We trace the history of rule-specific worst cases across seven representative
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