BayeSQP: Bayesian Optimization through Sequential Quadratic Programming

• URL: http://arxiv.org/abs/2602.03232v1
• Date: Tue, 03 Feb 2026 08:08:03 GMT
• Title: BayeSQP: Bayesian Optimization through Sequential Quadratic Programming
• Authors: Paul Brunzema, Sebastian Trimpe,
• Abstract summary: BayeSQP is a novel algorithm for general black-box optimization.<n>It combines the structure of sequential quadratic programming with concepts from Bayesian optimization.<n>BayeSQP outperforms state-of-the-art methods in high-dimensional settings.
• Score: 12.643071505470056
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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.

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