D. Li - School of Artificial Intelligence, Guangzhou Huashang College, Guangzhou 511300, China. S. Wang - School of Mathematics, Physics and Statistics, Baise University, Baise 533099, China.
This paper introduces a generalized relaxed-inertial conjugate gradient projection (CGP) algorithm for solving constrained nonlinear equations, which are widely encountered in practical applications. By integrating the relaxed-inertial mechanism with the projection technique and a modified Hager-Zhang-type conjugate parameter, the proposed algorithm generates the search direction that inherently satisfies sufficient descent condition and trust region feature without requiring any line search. The proposed algorithm is derivative-free, low-memory, and well-suited for large-scale equations. We establish the global convergence of the proposed algorithm under mild hypotheses, notably without the Lipschitz continuity requirement. Numerical results demonstrate the proposed algorithm's efficiency and competitiveness in large-scale constrained nonlinear equations, where it can solve approximately 68.06% of test problems with the fewest iterations, 85.00% with the fewest function evaluations, and 74.72% with the least running time in seconds. Furthermore, it is successfully applied to sparse signal reconstruction applications.
D. Li, S. Wang, A relaxed-inertial CGP algorithm with modified Hager-Zhang-type parameter for constrained nonlinear equations with its application, Journal of Mathematics and Computer Science, 42 (2026), no. 1, 21--42
Li D., Wang S., A relaxed-inertial CGP algorithm with modified Hager-Zhang-type parameter for constrained nonlinear equations with its application. J Math Comput SCI-JM. (2026); 42(1):21--42
Li, D., Wang, S.. "A relaxed-inertial CGP algorithm with modified Hager-Zhang-type parameter for constrained nonlinear equations with its application." Journal of Mathematics and Computer Science, 42, no. 1 (2026): 21--42
