Characterize the local-search landscape of simplex quadratic encodings

Characterize basin volumes under declared initialization distributions, convergence times, decoded-assignment quality, and the dependence of these quantities on offsets and search dynamics for the simplex quadratic formulations developed in the paper.

Background

The paper proves correspondences between local minima and combinatorial structures, including maximal cliques and, for complete factor-state models, all discrete assignments. These structural results do not determine how a particular continuous solver behaves dynamically. The authors explicitly identify basin volumes, convergence times, decoded-solution quality, and dependence on offsets and search dynamics as unresolved quantities requiring further characterization.

References

The unresolved quantities include basin volumes under a declared initialization distribution, convergence times, the quality of decoded assignments, and their dependence on offsets and search dynamics.

— Standard Quadratic Formulations of Many NP Problems: A Simplex-Based Compilation Framework for Combinatorial Optimization  (2610.01911 - Miri et al., 1 Oct 2026) in Section 11, subsection “Local landscape beyond cliques”