In this paper, we propose a new hybrid coefficient of conjugate gradient method (CG) for solving unconstrained optimization model. The is combination part the MMSIS (Malik et.al, 2020) and PRP (Polak, Ribi'ere \& Polyak, 1969) coefficients. Under exact line search, search direction satisfies sufficient descent condition based on certain assumption, establish global convergence properties. U...

Abstract In this study, we introduce a novel hybrid conjugate gradient [CG] to solve an efficient and effective unconstrained optimization problem. The parameter θ k is convex combination of the method <mml:mstyle ...

Conjugate gradient methods have been paid attention to, because they can be directly applied to large-scale unconstrained optimization problems. In order to incorporate second order information of the objective function into conjugate gradient methods, Dai and Liao (2001) proposed a conjugate gradient method based on the secant condition. However, their method does not necessarily generate a de...

We compare the performance of several robust large-scale minimization algorithms applied for the minimization of the cost functional in the solution of ill-posed inverse problems related to parameter estimation applied to the parabolized Navier-Stokes equations. The methods compared consist of the conjugate gradient method (CG), Quasi-Newton (BFGS), the limited memory Quasi-Newton (L-BFGS) [1],...

We compare the performance of several robust large-scale minimization algorithms for the unconstrained minimization of an ill-posed inverse problem. The parabolized Navier-Stokes equations model was used for adjoint parameter estimation. The methods compared consist of two versions of the nonlinear conjugate gradient method (CG), Quasi-Newton (BFGS), the limited memory Quasi-Newton (L-BFGS) [15...

Conjugate gradient methods are widely used for solving large-scale unconstrained optimization problems, because they do not need the storage of matrices. In this paper, we propose a general form of three-term conjugate gradient methods which always generate a sufficient descent direction. We give a sufficient condition for the global convergence of the proposed general method. Moreover, we pres...