We develop a unified level-bundle method, called accelerated constrained level-bundle (ACLB) algorithm, for solving constrained convex optimization problems. where the objective and constraint functions can be nonsmooth, weakly smooth, and/or smooth. ACLB employs Nesterov’s accelerated gradient technique, and hence retains the iteration complexity as that of existing bundle-type methods if the objective or one of the constraint functions is nonsmooth. More importantly, ACLB can significantly reduce iteration complexity when the objective and all constraints are (weakly) smooth. In addition, if the objective contains a nonsmooth component which can be written as a specific form of maximum, we show that the iteration complexity of this component can be much lower than that for general nonsmooth objective function. Numerical results demonstrate the effectiveness of the proposed algorithm.

中文翻译：

---

弱光滑凸约束优化中能级束方法的加速技术

我们开发了一种统一的级别捆绑方法，称为加速约束级别捆绑（ACLB）算法，用于解决约束凸优化问题。其中目标和约束函数可能是不平滑，弱平滑和/或平滑的。ACLB采用Nesterov的加速梯度技术，因此，如果目标或约束函数之一不平滑，则保留了与现有捆绑类型方法相同的迭代复杂性。更重要的是，当目标和所有约束（弱）平滑时，ACLB可以显着降低迭代复杂度。另外，如果目标包含可以写为最大值的特定形式的非平滑组件，则我们将表明该组件的迭代复杂度可以比一般的非平滑目标函数低。