A class of bilinear matrix constraint optimization problem and its applications

A broad class of minimization problems involving the sum of nonconvex and nonsmooth functions with a bilinear matrix equality constraint is introduced. The constraint condition can be regarded as a generalization of the multiplicative decomposition and additive decomposition of the original data. Augmented Lagrangian multiplier method and proximal alternating linearized minimization algorithm are applied for effectively solving the problem. Convergence guarantee is given under some mild assumptions. Taking two applications for instance to show that many practical problems can be converted to the general model with simple reformation, and effectively solved by the algorithm. The numerical experimental result shows the proposed method has better convergence property, better recovery result and less time-consuming than the compared methods. (C) 2021 Elsevier B.V. All rights reserved.