GLOBAL CONVERGENCE ANALYSIS OF A MODIFIED CONJUGATE GRADIENT METHOD FOR UNCONSTRAINED OPTIMIZATION PROBLEMS
Abstract
In this paper, the global convergence analysis of a modified conjugate gradient method for solving unconstrained optimization problems was considered. We proposed a modified conjugate gradient method for solving unconstrained optimization problems that incorporates an adaptive step size selection scheme. We analyze the method’s global convergence properties theoretically, demonstrating that it satisfies the sufficient descent and global convergence conditions under various assumptions. And we provide numerical experiments to illustrate its effectiveness and efficiency in solving unconstrained optimization problems. We also compare the numerical performance of the proposed method against three existing methods namely, FR, HS and PR using MATLAB simulations. The proposed method was found to perform better than FR and HS, and in competition with PR with respect to computation time, number of iteration and function evaluation.
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