Requiring LICQ/SCS/SOSC everywhere in bilevel optimization is non-prevalent and rigid, while holding almost everywhere is prevalent, but the distinction introduces fundamental difficulties.
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On the Nature of Regularity Assumptions in Bilevel Optimization with Constrained Lower-level Problem
Requiring LICQ/SCS/SOSC everywhere in bilevel optimization is non-prevalent and rigid, while holding almost everywhere is prevalent, but the distinction introduces fundamental difficulties.