论文标题
与单调夹杂物和非平滑优化问题有关的连续动力学
Continuous dynamics related to monotone inclusions and non-smooth optimization problems
论文作者
论文摘要
这项调查的目的是从用于求解单调包含和非平滑优化问题的一阶动力学系统的变异分析中介绍主要的重要技术和工具。微分方程通过分解（如果是最大单调集值算子）或非平滑函数的近端操作员表示。产生的轨迹的渐近分析取决于Lyapunov理论，在该理论中，适当的能量功能起着决定性作用。虽然本文的大部分与单调夹杂物和变化案例中的凸优化问题有关，但我们还为解决非凸优化问题的动态系统提供了结果，其中使用了Kurdyka-lojasiewicz属性。
The aim of this survey is to present the main important techniques and tools from variational analysis used for first and second order dynamical systems of implicit type for solving monotone inclusions and non-smooth optimization problems. The differential equations are expressed by means of the resolvent (in case of a maximally monotone set valued operator) or the proximal operator for non-smooth functions. The asymptotic analysis of the trajectories generated relies on Lyapunov theory, where the appropriate energy functional plays a decisive role. While the most part of the paper is related to monotone inclusions and convex optimization problems in the variational case, we present also results for dynamical systems for solving non-convex optimization problems, where the Kurdyka-Lojasiewicz property is used.
