论文标题
使用Lyapunov函数的加速梯度算法的凸合成量算法和鞍点问题
Convex Synthesis of Accelerated Gradient Algorithms for Optimization and Saddle Point Problems using Lyapunov functions
论文作者
论文摘要
本文考虑了设计基于梯度的加速算法以优化和鞍点问题的问题。目标函数类别由广义部门条件定义。这类功能包含Lipschitz梯度的强烈凸出功能，还包含非凸功能，这不仅允许解决优化问题，还可以解决鞍点问题。所提出的设计程序依赖于合适的Lyapunov函数和凸半准编程。所提出的合成允许设计达到最先进的加速梯度方法及以后的算法。
This paper considers the problem of designing accelerated gradient-based algorithms for optimization and saddle-point problems. The class of objective functions is defined by a generalized sector condition. This class of functions contains strongly convex functions with Lipschitz gradients but also non-convex functions, which allows not only to address optimization problems but also saddle-point problems. The proposed design procedure relies on a suitable class of Lyapunov functions and on convex semi-definite programming. The proposed synthesis allows the design of algorithms that reach the performance of state-of-the-art accelerated gradient methods and beyond.
