{"ID":2876034,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.01651","arxiv_id":"2509.01651","title":"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.","short_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...","url_abs":"https://arxiv.org/abs/2509.01651","url_pdf":"https://arxiv.org/pdf/2509.01651v4","authors":"[\"Gul Hameed\",\"Tao Chen\",\"Antonio del Rio Chanona\",\"Lorenz T. Biegler\",\"Michael Short\"]","published":"2025-09-01T17:53:06Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}