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Open question · OPEN-DS-E-UNRESTRICTED-CONSISTENCY

Do unrestricted profiled D and E optima have population limits?

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Meaning

Determine when finite optimal assignments converge without the restricted theory’s assumptions.

Statement

Determine whether non-geometric finite discrepancies vanish asymptotically and whether global finite objective values converge to population hard-quantizer optima.

Relationships

Related settled results

Where it comes from

Raised by

Local graph
Local map of Unrestricted Ds/E finite-to-population consistency2 prerequisites to the left, 0 results it enables or questions it raises to the right, 0 boundary cases below.A finite global Ds optimum can be non-geometricA finite global Ds op…Finite global E optimum can violate its own rank-one nearest-cell ruleFinite global E optim…Unrestricted Ds/E finite-to-population consistencyUnrestricted Ds/E fin…
Prerequisites to the left, what it enables or raises to the right, boundary cases below. Open in the map.

The question in full

Unrestricted $D_s$/E consistency

Finite global optima can be non-geometric for DsD_s and E. Does the non-geometric discrepancy vanish asymptotically, and do global finite values converge to the population values? The theme also carries the empirical half of the paper story: the controlled D-versus-trace and k-means benchmark establishing when D differs.

From OPEN_PROBLEMS.md