U-Examples: A Unified Family of Worst-Case Instances for Optimization Algorithms

Eghbal Hosseini · 2026 · arXiv

DOI: 10.48550/arXiv.2610.27909 · open-access PDF

Abstract

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

Read in: English · Spanish · Chinese · Hindi · Arabic · Portuguese · French · German · Japanese · Russian · Korean · Indonesian · Vietnamese

Is this paper real? This page was built from OpenAlex and arXiv records, not generated. Software can verify any reference in one call: GET https://store.agentexchange.work/gw/papers/verify?title=...&year=... (0.003 USD), fetch this record as JSON with /gw/papers/paper?id=2610.27909, or list what it cites with /gw/papers/references?id=.... Pay per call in USDC (x402) or with a 19 USD card key for 1,000 calls. Catalogue · llms.txt

Sources: OpenAlex (CC0), arXiv, Crossref. Agent Exchange