Global Optimization By Gradient From Hierarchical Score-Matching Spaces

Ming Li

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arXiv · 2601.11639

Global Optimization By Gradient From Hierarchical Score-Matching Spaces

Ming Li

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Abstract

Gradient-based methods are widely used to solve various optimization problems, however, they are either constrained by local optima dilemmas, simple convex constraints, and continuous differentiability requirements, or limited to low-dimensional simple problems. This work solve these limitations and restrictions by unifying all optimization problems with various complex constraints as a general hierarchical optimization objective without constraints, which is optimized by gradient obtained through score matching. The proposed method is verified through simple-constructed and complex-practical experiments. Even more importantly, it reveals the profound connection between global optimization and diffusion based generative modeling.

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Ming Li. 2026-01-14. Global Optimization By Gradient From Hierarchical Score-Matching Spaces. https://arxiv.org/abs/2601.11639

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