Neurodynamic approaches for sparse recovery problem with linear inequality constraints.
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This paper develops two neurodynamic approaches for solving the L1-minimization problem with the linear inequality constraints. First, a centralized neurodynamic approach is proposed based on projection operator and nonnegative quadrant. The stability and global convergence of the centralized neurodynamic approach are analyzed by the Lyapunov method in detail. Considering that the distributed optimization problem has the advantages of information protection and scalability, the L1-minimization problem with linear inequality constraints is transformed into a distributed sparse optimization problem under mild conditions. Then, using the centralized neurodynamic approach and multi-agent consensus theory, a distributed neurodynamic approach is proposed for the distributed optimization problem. Furthermore, relevant theories show that each agent globally converges to an optimal solution of the distributed optimization problem. Finally, the presented centralized neurodynamic approach is applied to sparse recovery problem with L-norm noise constraints and the effectiveness of distributed approach is shown by several experiments on sparse signal recovery.