# A Superlinearly Convergent Evolution Strategy

arXiv: https://arxiv.org/abs/2505.10987 · HTML: https://mlsanity.com/paper/2505.10987/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 May 2025.

## Built on by (most cited first, 1 of 1)

- [Performance and Explainability Requirements of Evolutionary Algorithms in Real-World Physics-Informed Optimization](https://mlsanity.com/paper/2605.28164/) (2026)

## Abstract (arXiv)

We present a hybrid algorithm between an evolution strategy and a quasi Newton method. The design is based on the Hessian Estimation Evolution Strategy, which iteratively estimates the inverse square root of the Hessian matrix of the problem. This is akin to a quasi-Newton method and corresponding derivative-free trust-region algorithms like NEWUOA. The proposed method therefore replaces the global recombination step commonly found in non-elitist evolution strategies with a quasi-Newton step. Numerical results show superlinear convergence, resulting in improved performance in particular on smooth convex problems.