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001052751 005__ 20260127203446.0
001052751 0247_ $$2doi$$a10.48550/ARXIV.2507.20769
001052751 037__ $$aFZJ-2026-01108
001052751 1001_ $$0P:(DE-HGF)0$$aZhang, Hongzhen$$b0
001052751 245__ $$aAccelerating Deterministic Global Optimization via GPU-parallel Interval Arithmetic
001052751 260__ $$barXiv$$c2025
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001052751 520__ $$aSpatial Branch and Bound (B&B) algorithms are widely used for solving nonconvex problems to global optimality, yet they remain computationally expensive. Though some works have been carried out to speed up B&B via CPU parallelization, GPU parallelization is much less explored. In this work, we investigate the design of a spatial B&B algorithm that involves an interval-based GPU-parallel lower bounding solver: The domain of each B&B node is temporarily partitioned into numerous subdomains, then massive GPU parallelism is leveraged to compute interval bounds of the objective function and constraints on each subdomain, using the Mean Value Form. The resulting bounds are tighter than those achieved via regular interval arithmetic without partitioning, but they remain fast to compute. We implement the method into our open-source solver MAiNGO via CUDA in two manners: wrapping all GPU tasks within one kernel function, or distributing the GPU tasks onto a CUDA graph. Numerical experiments show that using more subdomains leads to significantly tighter lower bounds and thus less B&B iterations. Regarding wall clock time, the proposed spatial B&B framework achieves a speedup of three orders of magnitude compared to applying interval arithmetic on the CPU without domain partitioning. Among the two implementations, the one developed with CUDA graph enables higher efficiency. Moreover, in some case studies, the proposed method delivers competitive or better performance compared to MAiNGO's default solver which is based on McCormick relaxations. These results highlight the potential of GPU-accelerated bounding techniques to accelerate B&B algorithms.
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001052751 650_7 $$2Other$$aOptimization and Control (math.OC)
001052751 650_7 $$2Other$$aDistributed, Parallel, and Cluster Computing (cs.DC)
001052751 650_7 $$2Other$$aFOS: Mathematics
001052751 650_7 $$2Other$$aFOS: Computer and information sciences
001052751 650_7 $$2Other$$a90C26, 90C30, 90-04, 90-08
001052751 7001_ $$0P:(DE-HGF)0$$aKerkenhoff, Tim$$b1
001052751 7001_ $$0P:(DE-HGF)0$$aKichler, Neil$$b2
001052751 7001_ $$0P:(DE-Juel1)172097$$aDahmen, Manuel$$b3$$ufzj
001052751 7001_ $$0P:(DE-Juel1)172025$$aMitsos, Alexander$$b4$$ufzj
001052751 7001_ $$0P:(DE-HGF)0$$aNaumann, Uwe$$b5
001052751 7001_ $$0P:(DE-HGF)0$$aBongartz, Dominik$$b6$$eCorresponding author
001052751 773__ $$a10.48550/ARXIV.2507.20769
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