Open question · OPEN-STRONGER-LOCAL-NEIGHBORHOODS

Can larger local moves improve the search?

Openpublication: open

Meaning

Study stronger neighbourhoods beyond single-observation relocation.

Statement

Analyze two-point swaps, move-two, merge-split, boundary perturbations, and rank-r updates; seek stronger guarantees and reduced multistart dependence.

Relationships

Related settled results

Exact weighted rank-two relocationD-RANK2-MOVE
Exact finite Ds one-point objective oracleDS-EXACT-MOVE-ORACLE

The full chain beneath it

Ds objective is the logdet of efficient/profiled Schur informationDS-SCHURdepth 2

Where it comes from

Raised by

Exact weighted rank-two relocationD-RANK2-MOVE
Exact finite Ds one-point objective oracleDS-EXACT-MOVE-ORACLE

Local graph

Prerequisites to the left, what it enables or raises to the right, boundary cases below. Open in the map.

The question in full

Stronger local neighborhoods

Two-point swaps, move-two, merge-split, boundary perturbations, rank- $r$ determinant updates: approximation guarantees, stronger geometry from 2-swap stability, reduced multistart dependence.

From OPEN_PROBLEMS.md