In this paper, the convergence analysis of a proposed new conjugate gradient method for unconstrained optimization problems was considered. This method inherits an important property of Polak-Ribiere-Polyak (PRP). Under the exact line search condition, we established the descent condition of the method as well as the global convergence of the method. Numerical results show that our formula is effective by comparing with some existing formulas.
In this paper, we propose a new hybrid conjugate gradient method for unconstrained optimization problems. The proposed method comprises of beta (DY), beta (WHY), beta (RAMI) and beta (New). The beta (New) was constructed purposely for this proposed hybrid method.The method possesses sufficient descent property irrespective of the line search. Under Strong Wolfe-Powell line search, we proved that the method is globally convergent. Numerical experimentation shows the effectiveness and robustness of the proposed method when compare with some hybrid as well as some modified conjugate gradient methods.
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