An <scp>LQR</scp>‐Lagrange Algorithm Generated by Interdisciplinary Integration With Optimal Control and Optimization

ABSTRACT Interdisciplinary integration is a superior method to improve the optimization algorithm. In this paper, control theory and optimization are combined, and the optimization algorithm is regarded as a control process. Based on the premise of optimal control, the state equation corresponding to Lagrange Algorithm is established with the Karush–Kuhn–Tucker (KKT) conditions as the objective. As an optimal control method, linear quadratic regulator (LQR) is utilized to control the calculation process, and an innovative LQR‐Lagrange Algorithm is proposed. The Lyapunov stability criterion is applied to analyze the convergence, and it is proved that the proposed LQR‐Lagrange Algorithm is bound to converge as long as the parameter matrices and are positive definite. The analysis indicates that the influence of parameters in LQR‐Lagrange Algorithm on the calculation speed is monotonic, and the elements in and has no effect on the convergence. Therefore, the proposed algorithm has a monotonic and user‐friendly parameter tuning strategy. It perfectly tackles the game between parameter tuning strategy and calculation speed, and cracks the difficulties and dilemmas of conventional algorithms in this issue, realizing a win‐win situation.