An Adaptive Neurodynamic Algorithm for Solving Matrix Valued Optimization Problem with Multiple Constraints

In this paper, an adaptive neurodynamic algorithm based on multi-agent system is proposed to solve the multi-constraint matrix-valued optimization problem. The optimization problem with linear matrix constraints AXB = H and specific inequality constraints can be equivalently reformulated as a distributed optimization problem using the penalty method and matrix decomposition. Furthermore, the adaptive penalty technique is introduced to enhance robustness and reduce computational cost. The problem is then solved using the improved Lagrangian function. Through theoretical analysis, we have proven that the equilibrium point of the proposed neural dynamics algorithm is the optimal solution to the matrix-valued optimization problem. Moreover, the equilibrium point of the neural dynamics algorithm is bounded and Lyapunov stable, with the algorithm state solution converging to the optimal solution of the matrix-valued optimization problem. Finaly, we provide a numerical example based on switching topologies in multi-agent systems. Numerical simulations validate the correctness of the theoretical results and demonstrate the capability to effectively solve the matrix-valued optimization problem under switching topology conditions.