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An approximate ADMM for solving linearly constrained nonsmooth optimization problems with two blocks of variables. (English) Zbl 1419.90082
Hosseini, Seyedehsomayeh (ed.) et al., Nonsmooth optimization and its applications. Based on the workshop “Nonsmooth Optimization and its Applications”, Bonn, Germany, May 15–19, 2017. Cham: Birkhäuser. ISNM, Int. Ser. Numer. Math. 170, 17-44 (2019).
Summary: Nonsmooth convex optimization problems with two blocks of variables subject to linear constraints are considered. A new version of the alternating direction method of multipliers (ADMM) is developed for solving these problems. In this method the subproblems are solved approximately. The convergence of the method is studied. New test problems are designed and used to verify the efficiency of the proposed method and to compare it with two versions of the proximal bundle method.
For the entire collection see [Zbl 1417.49001].

MSC:
90C25 Convex programming
49J52 Nonsmooth analysis
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