Global optimization tailored for graphics processing units: Complete and rigorous search for large-scale nonlinear minimization

[2507.01770] Global optimization tailored for graphics processing units: Complete and rigorous search for large-scale nonlinear minimization Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Numerical Analysis arXiv:2507.01770 (math) [Submitted on 2 Jul 2025 ( v1 ), last revised 13 Apr 2026 (this version, v4)] Title: Global optimization tailored for graphics processing units: Complete and rigorous search for large-scale nonlinear minimization Authors: Guanglu Zhang , Qihang Shan , Jonathan Cagan View a PDF of the paper titled Global optimization tailored for graphics processing units: Complete and rigorous search for large-scale nonlinear minimization, by Guanglu Zhang and 2 other authors View PDF Abstract: This paper introduces a numerical method to enclose the global minimum of a nonlinear function subject to simple bounds on the variables. Using interval analysis, coupled with the computational power and architecture of graphics processing units (GPUs), the method iteratively rules out the regions in the search domain where the global minimum cannot exist and leaves a finite set of regions where the global minimum must exist. For effectiveness, because of the rigor of interval analysis, the method is guaranteed to enclose the global minimum even in the presence of rounding errors. For efficiency, the method employs a novel GPU-based single program, single data parallel programming style to circumvent major GPU performance bottlenecks, and a variable cycling technique is also integrated into the method to reduce computational cost when minimizing large-scale nonlinear functions. The method is validated by minimizing 11 benchmark test functions with scalable dimensions, including the well-known Ackley function, Griewank function, Levy function, Rastrigin function, and Rosenbrock function. These benchmark test functions represent grand challenges of global optimization, and enclosing the guaranteed global minimum of these benchmark test functions with more than 80 dimensions has not been reported in the literature. Our method completely searches the feasible domain and successfully encloses the guaranteed global minimum of these 11 benchmark test functions with up to 10,000 dimensions using only one GPU in a reasonable computation time, far exceeding the reported results in the literature due to the unique method design and implementation based on GPU architecture. Comments: 35 pages, 4 figures Subjects: Numerical Analysis (math.NA) ; Artificial Intelligence (cs.AI); Distributed, Parallel, and Cluster Computing (cs.DC); Mathematical Software (cs.MS); Optimization and Control (math.OC) MSC classes: 65G20, 65G30, 65G40, 90C06, 90C26, 90C30 ACM classes: G.1.6; G.4 Cite as: arXiv:2507.01770 [math.NA] (or arXiv:2507.01770v4 [math.NA] for this version) https://doi.org/10.48550/arXiv.2507.01770 Focus to learn more arXiv-issued DOI via DataCite Journal reference: PNAS Nexus, 5(4), pp. pgag103 (2026) Related DOI : https://doi.org/10.1093/pnasnexus/pgag103 Focus to learn more DOI(s) linking to related resources Submission history From: Guanglu Zhang [ view email ] [v1] Wed, 2 Jul 2025 14:54:52 UTC (1,503 KB) [v2] Mon, 7 Jul 2025 15:10:52 UTC (1,503 KB) [v3] Thu, 8 Jan 2026 20:50:38 UTC (655 KB) [v4] Mon, 13 Apr 2026 19:14:59 UTC (1,182 KB) Full-text links: Access Paper: View a PDF of the paper titled Global optimization tailored for graphics processing units: Complete and rigorous search for large-scale nonlinear minimization, by Guanglu Zhang and 2 other authors View PDF view license Current browse context: math.NA < prev | next > new | recent | 2025-07 Change to browse by: cs cs.AI cs.DC cs.MS cs.NA math math.OC References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... 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