Global convergence of modified conjugate gradient methods with application in conditional model regression function

The conjugate gradient method is one of the most important ideas in sci-entific computing. It is applied to solving linear systems of equations and nonlinear optimization problems. In this paper, based on a variant of the Hestenes–Stiefel (HS) method and Polak–Ribière–Polyak (PRP) method, two modified conjugate gradient methods (named MHS∗ and MPRP∗) are presented and analyzed. The search direction of the presented methods fulfills the sufficient descent condition at each iteration. We establish the global convergence of the proposed algorithms under normal assumptions and strong Wolfe line search. Preliminary elementary numerical experi-ment results are presented, demonstrating the promise and the effective-ness of the proposed methods. Finally, the proposed methods are further extended to solve the problem of conditional model regression function.