Two improved nonlinear conjugate gradient methods with application in conditional model regression function

The conjugate gradient (CG) method is one of the most important ideas in scientific computing, it is applied to solve linear systems of equations and nonlinear optimization problems. In this paper, based on a variant of Dai-Yuan (DY) method and Fletcher-Reeves (FR) method, two modified CG methods (named IDY and IFR) 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 experiment results are presented, demonstrating the promise and the effectiveness of the proposed methods. Finally, the proposed methods are further extended to solve the problem of conditional model regression function.