preprint · arXiv (Cornell University) · 2026

BayeSQP: Bayesian Optimization through Sequential Quadratic Programming

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Abstract

We introduce BayeSQP, a novel algorithm for general black-box optimization that merges the structure of sequential quadratic programming with concepts from Bayesian optimization. BayeSQP employs second-order Gaussian process surrogates for both the objective and constraints to jointly model the function values, gradients, and Hessian from only zero-order information. At each iteration, a local subproblem is constructed using the GP posterior estimates and solved to obtain a search direction. Crucially, the formulation of the subproblem explicitly incorporates uncertainty in both the function and derivative estimates, resulting in a tractable second-order cone program for high probability improvements under model uncertainty. A subsequent one-dimensional line search via constrained Thompson sampling selects the next evaluation point. Empirical results show thatBayeSQP outperforms state-of-the-art methods in specific high-dimensional settings. Our algorithm offers a principled and flexible framework that bridges classical optimization techniques with modern approaches to black-box optimization.

Cite this paper

APA 7

Brunzema, P., & Trimpe, S. (2026). BayeSQP: Bayesian Optimization through Sequential Quadratic Programming. arXiv (Cornell University). https://doi.org/10.48550/arxiv.2602.03232

MLA 9

Brunzema, Paul, and Sebastian Trimpe. “BayeSQP: Bayesian Optimization through Sequential Quadratic Programming.” arXiv (Cornell University), 2026, https://doi.org/10.48550/arxiv.2602.03232.

Chicago

Brunzema, Paul, and Sebastian Trimpe. 2026. “BayeSQP: Bayesian Optimization through Sequential Quadratic Programming.” arXiv (Cornell University). https://doi.org/10.48550/arxiv.2602.03232.

Harvard

Brunzema, P. and Trimpe, S. (2026) ‘BayeSQP: Bayesian Optimization through Sequential Quadratic Programming’, arXiv (Cornell University). Available at: https://doi.org/10.48550/arxiv.2602.03232.

BibTeX

@misc{brunzema2026bayesqp,
  title = {{BayeSQP: Bayesian Optimization through Sequential Quadratic Programming}},
  author = {Brunzema, Paul and Trimpe, Sebastian},
  journal = {arXiv (Cornell University)},
  year = {2026},
  doi = {10.48550/arxiv.2602.03232}
}

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