Certifiable global optimality under outlier-contaminated measurements

Establish certifiably correct and globally optimal solutions for robotic perception problems involving outliers, such as robust multi-robot SLAM with outlier-corrupted loop closures.

Background

The paper evaluates SPARSER on robust multi-robot SLAM datasets containing naturally occurring outliers and uses iteratively reweighted least squares within a graduated non-convexity schedule. Although this procedure improves robustness to initialization and enables successful numerical optimization, the resulting solutions are not accompanied by a certificate of global optimality. The authors explicitly identify the existence of certifiably correct and globally optimal solutions in the presence of outliers as unresolved, distinguishing this setting from the outlier-free problems considered elsewhere in the evaluation.

References

Unlike the outlier-free setting, certifiably correct and globally optimal solutions under outliers remain an open problem.

— SPARSER: Sparse Variable Projection by Exploiting Separable Structure in Robotic Perception  (2609.24708 - Sanderson et al., 21 Sep 2026) in Section 4, subsection “Robust optimization on real-world SLAM data with outliers”