A Bregman alternating direction method of multipliers for sparse probabilistic Boolean network problem

The main task of genetic regulatory networks is to construct a sparse probabilistic Boolean network (PBN) based on a given transition-probability matrix and a set of Boolean networks (BNs). In this paper, a Bregman alternating direction method of multipliers (BADMM) is proposed to solve the minimization problem raised in PBN. All the customized subproblemsolvers of the BADMM do not involve matrix multiplication, consequently the proposed method is in a position to deal with some huge-scale problems. The convergence to stationary point of the BADMM is proved under some mild conditions. Numerical experiments show that the BADMM is effective and efficient comparing with some existing methods.

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