Joint optimization of Hessian-sampling and CBO query budgets

Determine the optimal allocation of a fixed objective-function query budget between Hessian sampling for estimating the linearly separable coordinate system and the subsequent consensus-based optimization stage.

Background

The numerical experiments reserve a substantial portion of the total query budget for finite-difference Hessian estimation, leaving the remainder for consensus-based optimization. The effectiveness of the overall method therefore depends on how these queries are divided between structural estimation and optimization.

The paper reports that a more detailed study of the optimal allocation and the influence of coordinate-estimation errors remains unresolved.

References

A more detailed numerical study regarding optimal query allocation (for Hessian sampling and CBO) and the influence of possible matrix estimation errors is left for future work.

— Consensus-based optimization for linearly separable functions  (2609.01317 - Fiedler et al., 1 Sep 2026) in Section 4, Experiments