University of Guilan Journal of Mathematical Modeling 2345-394X 8 1 2020 03 01 A modified conjugate gradient method based on a modified secant equation 1 20 3760 10.22124/jmm.2019.14807.1343 EN Parvaneh Faramarzi Department of Mathematics, Faculty of Science, Razi University, Kermanshah, Iran Keyvan Amini Department of Mathematics, Faculty of Science, Razi University, Kermanshah, Iran Journal Article 2019 10 22 Quasi-Newton methods are one of the popular iterative schemes to solve unconstrained optimization problems. The high convergence rate and excellent precision are two prominent characteristics of the quasi-Newton methods. In this paper, according to the preferable properties of a modified secant condition, a modified conjugate gradient method is introduced. The new algorithm satisfies the sufficient descent property independent of the line search. The convergence properties of the proposed algorithm are investigated both for uniformly convex and general functions. Numerical experiments show the superiority of the proposed method.<br /><br /> Conjugate gradient methods Modified secant condition Sufficient descent condition Global convergence https://jmm.guilan.ac.ir/article_3760_54f21bccf7cdd505f59d0dbfe14a9ec8.pdf