A class of customized proximal point algorithms for linearly constrained convex optimization
A class of customized proximal point algorithms for linearly constrained convex optimization
复制标题
一类用于线性约束凸优化的定制近点算法
DOI：
10.1007/s40314-016-0371-3
复制
发表时间：
2018-05-01
影响因子：
2.6
通讯作者：
Ni, Mingfang
中科院分区：
文献类型：
--
作者：
Ma, Feng;Ni, Mingfang
针对线性约束凸优化问题，提出了一类自定义邻近点算法。该算法是可实现的，只要目标函数的邻近算子容易评估。我们表明，通过算法标量的特殊设置，我们的算法包含定制的邻近点算法（He等人，Optim Appl 56：559-572，2013）、线性化增广拉格朗日方法（Yang和Yuan，Math Comput 82：301-329，2013）、Bregman算子分裂算法（Zhang等人，SIAM J Imaging Sci 3：253-276，2010）作为特例。证明了算法的全局收敛性和最坏情况下的收敛速度。数值结果表明，该算法在很宽的标量范围内都能很好地工作。
In this paper, we propose a class of customized proximal point algorithms for linearly constrained convex optimization problems. The algorithms are implementable, provided that the proximal operator of the objective function is easy to evaluate. We show that, with special setting of the algorithmic scalar, our algorithms contain the customized proximal point algorithm (He et al., Optim Appl 56:559–572, 2013), the linearized augmented Lagrangian method (Yang and Yuan, Math Comput 82:301–329, 2013), the Bregman Operator Splitting algorithm (Zhang et al., SIAM J Imaging Sci 3:253–276, 2010) as special cases. The global convergence and worst-case convergence rate measured by the iteration complexity are established for the proposed algorithms. Numerical results demonstrate that the algorithms work well for a wide range of the scalar.