论文标题
从坐标降低一般能量功能的轨迹收敛性
Trajectory Convergence from Coordinate-wise Decrease of General Energy Functions
论文作者
论文摘要
我们考虑受坐标能量减少的任意轨迹：每个条目的衍生物的符号永远不会与某些能量函数的梯度的相应条目的符号相同。我们表明，这种简单的条件可以确保收敛到一个点，至少能量函数，或者在其Hessian具有非常特定属性的集合中。这扩展并加强了最新结果，这些结果仅限于凸二次能量函数。我们通过使用它来证明结果的应用来证明我们的结果的应用，以证明遭受多个不确定性的一类多机构系统的收敛性。
We consider arbitrary trajectories subject to a coordinate-wise energy decrease: the sign of the derivative of each entry is never the same as that of the corresponding entry of the gradient of some energy function. We show that this simple condition guarantees convergence to a point, to the minimum of the energy functions, or to a set where its Hessian has very specific properties. This extends and strengthens recent results that were restricted to convex quadratic energy functions. We demonstrate the application of our result by using it to prove the convergence of a class of multi-agent systems subject to multiple uncertainties.
