Trust-region filter algorithms utilizing Hessian information for gray-box optimization

Abstract

Optimizing industrial processes often involves gray-box models that couple algebraic glass-box equations with black-box components lacking analytic derivatives. Such systems challenge derivative-based solvers. The classical trust-region filter (TRF) algorithm provides a robust framework but requires extensive parameter tuning and numerous black-box evaluations. This work introduces four Hessian-informed TRF variants that use projected positive definite Hessians for automatic step scaling and minimal tuning, combined with both low-fidelity (linear, quadratic) and high-fidelity (Taylor series, Gaussian process) surrogates for local black-box approximation. Tested on 25 gray-box benchmarks and five engineering case studies, the new variants achieved up to order-of-magnitude reductions in iterations and black-box evaluations, with reduced sensitivity to tuning parameters relative to the classical TRF algorithm. High-fidelity surrogates solved 92%–100% of problems, compared with 72%–84% for low-fidelity surrogates. The developed TRF methods also outperformed classical derivative-free optimization solvers. Results show that new variants offer robust, scalable alternatives for gray-box optimization.