论文标题
efix：用于分布式优化的精确固定点方法
EFIX: Exact Fixed Point Methods for Distributed Optimization
论文作者
论文摘要
我们考虑在连接的网络上强烈凸出分布的共识优化。 Efix是提出的方法，是使用二次惩罚方法得出的。更详细地说，我们使用标准重新制定{将原始问题转换为更高维空间中的受约束问题{{以增加惩罚参数的增加，定义了一系列合适的二次惩罚子问题。对于二次目标，相应的序列由二次惩罚子问题组成。对于通用强烈凸状情况，目标函数用二次模型近似，因此所产生的惩罚子问题的序列再次是二次的。然后，通过通过固定点（R） - 线性求解器（例如Jacobi过度删除方法）求解每个二次惩罚子问题来得出EFIX。证明了确切的收敛性以及二次情况下o（epsilon^-1）的最坏情况的复杂性。在强烈凸出通用函数的情况下，获得了惩罚方法的标准结果。数值结果表明，该方法具有最先进的一阶方法具有高度竞争力，需要较小的计算和通信工作，并且可以选择算法参数。
We consider strongly convex distributed consensus optimization over connected networks. EFIX, the proposed method, is derived using quadratic penalty approach. In more detail, we use the standard reformulation { transforming the original problem into a constrained problem in a higher dimensional space { to define a sequence of suitable quadratic penalty subproblems with increasing penalty parameters. For quadratic objectives, the corresponding sequence consists of quadratic penalty subproblems. For the generic strongly convex case, the objective function is approximated with a quadratic model and hence the sequence of the resulting penalty subproblems is again quadratic. EFIX is then derived by solving each of the quadratic penalty subproblems via a fixed point (R)-linear solver, e.g., Jacobi Over-Relaxation method. The exact convergence is proved as well as the worst case complexity of order O(epsilon^-1) for the quadratic case. In the case of strongly convex generic functions, a standard result for penalty methods is obtained. Numerical results indicate that the method is highly competitive with state-of-the-art exact first order methods, requires smaller computational and communication effort, and is robust to the choice of algorithm parameters.
