A Robust IEP-Based Optimization Framework Toward Large-Scale Coupling Matrix Reconfiguration

The conventional inverse eigenvalue problem (IEP)-based optimization model has proven effective for various coupling matrix (CM) reconfigurations. However, its mathematical foundations remain unclear, and it suffers from significant limitations, including high sensitivity to initial values and a tendency to converge to local optima, especially for large-scale problems. This study not only revisits and elucidates the mathematical theory underlying this approach but also introduces a novel IEP-based optimization model that uses a strictly diagonally dominant matrix and parameter reduction to reduce sensitivity to initial values. In addition, the “<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">uphill move</i>” strategy is integrated into the damped Levenberg–Marquardt (LM) optimization method to facilitate escape from local minima and accelerate convergence. Extensive numerical experiments validate the proposed optimization framework, demonstrating its rapid convergence and robustness, particularly in scenarios with large-scale problems and varying initial values.