For nonlinear nonsmooth DC programming (difference of convex functions), we introduce a new redistributed proximal bundle method. The subgradient information of both the DC components is gathered from some neighbourhood of the current stability center and it is used to build separately an approximation for each component in the DC representation. Especially we employ the nonlinear redistributed technique to model the second component of DC function by constructing a local convexification cutting plane. The corresponding convexification parameter is adjusted dynamically and is taken sufficiently large to make the `augmented' linearization errors nonnegative. Based on above techniques we obtain a new convex cutting plane model of the original objective function. Based on this new approximation the redistributed proximal bundle method is designed and the convergence of the proposed algorithm to a Clarke stationary point is proved. A simple numerical experiment is given to show the validity of the presented algorithm.

中文翻译：

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一种基于局部凸化模型的非线性非光滑直流规划的重分布丛算法

对于非线性非光滑 DC 规划（凸函数的差分），我们引入了一种新的重分布近端丛方法。两个 DC 分量的次梯度信息是从当前稳定中心的某个邻域收集的，它用于分别为 DC 表示中的每个分量构建近似值。特别是我们采用非线性重分布技术，通过构造局部凸化切割平面来模拟 DC 函数的第二分量。相应的凸化参数是动态调整的，并且取得足够大以使“增强的”线性化误差为非负。基于上述技术，我们获得了原始目标函数的新凸切割平面模型。基于这种新的近似，设计了重新分布的近端丛方法，并证明了所提出的算法对克拉克驻点的收敛性。给出了一个简单的数值实验来证明所提出算法的有效性。