A new conjugate gradient algorithm for nonconvex minimization problem and its convergence properties

Abstract The primary objective of this paper is to develop a novel and efficient modified conjugate gradient algorithm for addressing nonconvex minimization problems. The study demonstrates that the proposed method exhibits a sufficient descent property regardless of the specific line search techniques employed. Furthermore, the algorithm is globally convergent towards solving the given problem, employing both Wolfe and Armijo line search techniques. To reinforce its efficacy, a numerical example is presented, utilizing image restoration problem.