A hybrid Bregman alternating direction method of multipliers for the linearly constrained difference-of-convex problems

Kai Tu (), Haibin Zhang (), Huan Gao () and Junkai Feng ()
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Kai Tu: Beijing University of Technology
Haibin Zhang: Beijing University of Technology
Huan Gao: Hunan First Normal University
Junkai Feng: Beijing University of Technology

Journal of Global Optimization, 2020, vol. 76, issue 4, No 2, 665-693

Abstract: Abstract In this paper, we propose a hybrid Bregman alternating direction method of multipliers for solving the linearly constrained difference-of-convex problems whose objective can be written as the sum of a smooth convex function with Lipschitz gradient, a proper closed convex function and a continuous concave function. At each iteration, we choose either subgradient step or proximal step to evaluate the concave part. Moreover, the extrapolation technique was utilized to compute the nonsmooth convex part. We prove that the sequence generated by the proposed method converges to a critical point of the considered problem under the assumption that the potential function is a Kurdyka–Łojasiewicz function. One notable advantage of the proposed method is that the convergence can be guaranteed without the Lischitz continuity of the gradient function of concave part. Preliminary numerical experiments show the efficiency of the proposed method.

Keywords: Linearly constrained difference-of-convex problems; Bregman distance; Alternating direction method of multipliers; Kurdyka–Łojasiewicz function (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10898-019-00828-4

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