A Decomposition-Based Data-Driven Branch-and-Bound Approach for Black-Box Global Optimization
Abstract
Many scientific and engineering applications require the global optimization of expensive black-box functions. In high-dimensional settings, however, achieving computational scalability is a major challenge. To address this challenge, we propose a distributed spatial branch-and-bound framework that exploits partially separable structure for the global optimization of box-constrained black-box problems. The proposed framework adopts a two-layer structure in which branching is performed only on a lower-dimensional set of coupling variables in an outer layer. Within each outer node, the remaining non-overlapping (private) variables, which appear independently across blocks, have their domains partitioned and explored in parallel within an inner layer, resulting in a naturally parallelizable framework that is well suited for implementation on multi-core CPU architectures. At each node, valid upper bounds are obtained via sampling, with optional refinement using a local solver, while lower bounds are computed using data-driven convex underestimators constructed over partitions of the private variables. A residual-based correction and finite-sample validity analysis provide conditions under which the partitionwise underestimators are valid lower bounds, while the proposed branching and refinement mechanism establishes convergence to an ε-global optimum. Numerical studies on benchmark and ODE-constrained parameter-estimation problems demonstrate improvements in both sampling efficiency and computational performance relative to monolithic approaches.
Related
- B3-PWL: GPU-Batched Branch-and-Bound for Piecewise-Linear Optimization with SOS2 Constraints
- Global Optimization of Mixed-Integer Bound-Constrained Quadratic Fractional Problems
- Adaptive Decomposition and Dual-Branch Linear Forecasting for Stock Price Prediction
- First-Order Primal-Dual Repairs for Scalable Branch and Bound
- Exact computation of the network modularity with branch-and-bound
BibTeX
@misc{fasiku2026decompositionbased,
title = {{A Decomposition-Based Data-Driven Branch-and-Bound Approach for Black-Box Global Optimization}},
author = {Damilola Fasiku and Wentao Tang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20539},
eprint = {2610.20539},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20539},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Decomposition-Based Data-Driven Branch-and-Bound Approach for Black-Box Global Optimization
AU - Damilola Fasiku
AU - Wentao Tang
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20539
UR - https://arxiv.org/abs/2610.20539
AB - Many scientific and engineering applications require the global optimization of expensive black-box functions. In high-dimensional settings, however, achieving computational scalability is a major challenge. To address this challenge, we propose a distributed spatial branch-and-bound framework that exploits partially separable structure for the global optimization of box-constrained black-box problems. The proposed framework adopts a two-layer structure in which branching is performed only on a lower-dimensional set of coupling variables in an outer layer. Within each outer node, the remaining non-overlapping (private) variables, which appear independently across blocks, have their domains partitioned and explored in parallel within an inner layer, resulting in a naturally parallelizable framework that is well suited for implementation on multi-core CPU architectures. At each node, valid upper bounds are obtained via sampling, with optional refinement using a local solver, while lower bounds are computed using data-driven convex underestimators constructed over partitions of the private variables. A residual-based correction and finite-sample validity analysis provide conditions under which the partitionwise underestimators are valid lower bounds, while the proposed branching and refinement mechanism establishes convergence to an ε-global optimum. Numerical studies on benchmark and ODE-constrained parameter-estimation problems demonstrate improvements in both sampling efficiency and computational performance relative to monolithic approaches.
ER -