Optimization Algorithm for Polynomial Approximation Models Based on Partial Coefficient Correction

To balance the computational cost of single-step iteration and fully utilize the efficiency advantage of the quadratic polynomial approximation model in algorithm design, this paper proposes and tests derivative-free optimization algorithms for five types of partial coefficient correction in polynomial approximation models, including hub-spoke, hinge, closed loop, spoke, and support wheel. Specifically, a random strategy is introduced during the implementation of the algorithm. Numerical experiments demonstrate the effectiveness of the algorithm and the efficiency differences between different methods.