提出新型投影算子，用于非凸优化的高效求解
A Bregman firmly nonexpansive proximal operator for baryconvex optimization
- 通过最小最大策略更新权重，构造新投影算子
- 该算子在混合几何下具有强非扩张性，固定点对应临界点
- 推导出连续动力系统，适合非凸优化问题分析
我们提出一种基于凸目标函数凸组合的投影算子的推广形式，其中系数通过最小最大方式更新。证明了该新算子相对于结合欧氏与信息几何的Bregman散度是Bregman强非扩张的；其不动点对应某一非凸函数的临界点。最后，推导出相关的连续流。
原文摘要 · Abstract (English)
We present a generalization of the proximal operator defined through a convex combination of convex objectives, where the coefficients are updated in a minimax fashion. We prove that this new operator is Bregman firmly nonexpansive with respect to a Bregman divergence that combines Euclidean and information geometries; and that its fixed points are given by the critical points of a certain nonconvex function. Finally, we derive the associated continuous flows.
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