Recently, it was posited that disparate optimization algorithms may be coalesced in terms of a central source emanating from optimal control theory. Here we further this proposition by showing how coordinate descent algorithms may be derived from this emerging new principle. In particular, we show that basic coordinate descent algorithms can be derived using a maximum principle and a collection of max functions as "control" Lyapunov functions. The convergence of the resulting coordinate descent algorithms is thus connected to the controlled dissipation of their corresponding Lyapunov functions. The operational metric for the search vector in all cases is given by the Hessian of the convex objective function.

翻译：最近，有观点认为不同优化算法可能源于最优控制理论这一统一框架。本文通过展示如何从这一新兴原理中推导坐标下降算法，进一步推进该命题。具体而言，我们证明基本坐标下降算法可通过极大值原理及一组作为"控制"李雅普诺夫函数的极大值函数推导得出。由此产生的坐标下降算法的收敛性，与其对应李雅普诺夫函数的受控耗散相关联。在所有情形下，搜索向量的操作度量均由凸目标函数的黑塞矩阵给出。