Construction of Uniform Designs over a Domain with Linear Constraints

Luojing Yang, Xiaoping Yang and Yongdao Zhou ()
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Luojing Yang: School of Statistics and Data Science, LPMC & KLMDASR, Nankai University, Tianjin 300071, China
Xiaoping Yang: National Elite Institute of Engineering, Northwestern Polytechnical University, Xi’an 710072, China
Yongdao Zhou: School of Statistics and Data Science, LPMC & KLMDASR, Nankai University, Tianjin 300071, China

Mathematics, 2025, vol. 13, issue 3, 1-23

Abstract: Uniform design is a powerful and robust experimental methodology that is particularly advantageous for multidimensional numerical integration and high-level experiments. As its applications expand across diverse disciplines, the theoretical foundation of uniform design continues to evolve. In real-world scenarios, experimental factors are often subject to one or more linear constraints, which pose challenges in constructing efficient designs within constrained high-dimensional experimental spaces. These challenges typically require sophisticated algorithms, which may compromise uniformity and robustness. Addressing these constraints is critical for reducing costs, improving model accuracy, and identifying global optima in optimization problems. However, existing research primarily focuses on unconstrained or minimally constrained hypercubes, leaving a gap in constructing designs tailored to arbitrary linear constraints. This study bridges this gap by extending the inverse Rosenblatt transformation framework to develop innovative methods for constructing uniform designs over arbitrary hyperplanes and hyperspheres within unit hypercubes. Explicit construction formulas for these constrained domains are derived, offering simplified calculations for practitioners and providing a practical solution applicable to a wide range of experimental scenarios. Numerical simulations demonstrate the feasibility and effectiveness of these methods, setting a new benchmark for uniform design in constrained experimental regions.

Keywords: mixture design; central composite discrepancy; inverse Rosenblatt transformation; constrained hypercubes (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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