A PRIMAL-DUAL SPLITTING ALGORITHM FOR FINDING ZEROS OF SUMS OF MAXIMAL MONOTONE OPERATORS
A PRIMAL-DUAL SPLITTING ALGORITHM FOR FINDING ZEROS OF SUMS OF MAXIMAL MONOTONE OPERATORS
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DOI：
10.1137/12088255x
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发表时间：
2013-01-01
影响因子：
3.1
通讯作者：
Heinrich, Andre
中科院分区：
文献类型：
--
作者：
Bot, Radu Ioan;Csetnek, Erno Robert;Heinrich, Andre
我们考虑了寻找一个极大单调算子和的零点的原始问题，以及另一个极大单调算子与线性连续算子的合成问题。通过对其Atouch-Thera型对偶包含问题的形式化描述，提出了有限维空间中同时求解这两个问题的原始-对偶分裂算法。该方案在每次迭代中分别使用最大单调算子的预解，克服了经典分裂算法在处理极大单调算子和线性连续算子组合时的不足。迭代算法用于解决图像处理和选址理论中出现的不可微凸优化问题。
We consider the primal problem of finding the zeros of the sum of a maximal monotone operator and the composition of another maximal monotone operator with a linear continuous operator. By formulating its Attouch-Thera-type dual inclusion problem, a primal-dual splitting algorithm which simultaneously solves the two problems in finite-dimensional spaces is presented. The proposed scheme uses at each iteration the resolvents of the maximal monotone operators involved in separate steps and aims to overcome the shortcoming of classical splitting algorithms when dealing with compositions of maximal monotone and linear continuous operators. The iterative algorithm is used for solving nondifferentiable convex optimization problems arising in image processing and in location theory.