MathDB3 problems
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Pataki's conjecture that facially exposed cones are nice
Pataki's conjecture. Facial exposedness and niceness are equivalent: every facially exposed closed convex cone is nice.
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The conjecture that bilateral facial reduction recovers and generalizes facial reduction and the Extended Dual System
Bilateral facial reduction conjecture. Many aspects of Facial Reduction and the Extended Dual System can be recovered—and potentially generalized—from the results developed in this…
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The niceness–facial exposedness conjecture for closed convex cones
Niceness–facial exposedness conjecture. Nice cones and facially exposed cones are the same class of cones.