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. B...
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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 lagrangealgorithm 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 Q and R 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 Q and R 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.
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