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.

翻译：梯度方法被广泛应用于求解各类优化问题，然而它们或受限于局部最优困境、简单凸约束及连续可微性要求，或局限于低维简单问题。本研究通过将所有含复杂约束的优化问题统一为无约束的通用层级优化目标，并利用基于得分匹配的梯度进行优化，从而克服了上述局限与限制。所提方法通过简单构造实验与复杂实际实验得到验证。更为重要的是，该方法揭示了全局优化与基于扩散的生成建模之间的深刻联系。