论文标题
全局优化的群梯度动力学：密度情况
Swarm gradient dynamics for global optimization: the density case
论文作者
论文摘要
使用非概念问题的共同几何和随机重新进行重新制定，并利用Monge-Kantorovich梯度系统制定使用消失的力，我们正式将模拟退火方法扩展到了一类广泛的全球优化方法。由于类似梯度的策略和颗粒相互作用的内置组合，我们称它们为群梯度动力学。就像在Holley-Kusuoka-Strocock的原始论文中一样，存在时间表的关键确保与全球最小化的融合是一种功能上的不平等。我们的核心理论贡献之一是证明了一维紧凑型歧管的这种不平等。我们猜想在更广泛的环境中不等式是正确的。我们还描述了一种通用方法，允许全球优化并证明功能不平等的关键作用{à} la la llojasiewicz。
Using jointly geometric and stochastic reformulations of nonconvex problems and exploiting a Monge-Kantorovich gradient system formulation with vanishing forces, we formally extend the simulated annealing method to a wide class of global optimization methods. Due to an inbuilt combination of a gradient-like strategy and particles interactions, we call them swarm gradient dynamics. As in the original paper of Holley-Kusuoka-Stroock, the key to the existence of a schedule ensuring convergence to a global minimizer is a functional inequality. One of our central theoretical contributions is the proof of such an inequality for one-dimensional compact manifolds. We conjecture the inequality to be true in a much wider setting. We also describe a general method allowing for global optimization and evidencing the crucial role of functional inequalities {à} la Łojasiewicz.
