<span>In this article, we give a new modification for the Dai-Liao method to solve monotonous nonlinear problems. In our modification, relied on two important procedures, one of them was projection and second damping quasi-Newton condition. The approach derivation yields parameters conjugated gradient direction which, through some conditions, have demonstrated sufficient descent property ...

Conjugate Gradient (CG) method is the most prominent iterative mathematical technique that can be useful for optimization of both linear and non-linear systems due to its simplicity, low memory requirement, computational cost, global convergence properties. However, some classical CG methods have drawbacks which include weak convergence, poor numerical performance in terms number iterations CPU...

In this paper we suggest a new conjugate gradient algorithm that for all both the descent and the conjugacy conditions are guaranteed. The search direction is selected as a linear combination of 0 k ≥ 1 k g + − and where , k s 1 1 ( ) k k g f x + + = ∇ , and the coefficients in this linear combination are selected in such a way that both the descent and the conjugacy condition are satisfied at ...

Abstract We study the use of inverse harmonic Rayleigh quotients with target for stepsize selection in gradient methods nonlinear unconstrained optimization problems. This not only provides an elegant and flexible framework to parametrize reinterpret existing schemes, but it also gives inspiration new tunable families steplengths. In particular, we analyze extend adaptive Barzilai–Borwein metho...

It is well known that conjugate gradient methods are useful for solving large-scale unconstrained nonlinear optimization problems. In this paper, we consider combining the best features of two methods. particular, give a new method, based on hybridization DY (Dai-Yuan), and HZ (Hager-Zhang) The hybrid parameters chosen such proposed method satisfies conjugacy sufficient descent conditions. show...

in this paper, the conjugate gradient method coupled with adjoint problem is used in order to solve the inverse heat conduction problem and estimation of the time- dependent heat flux using the temperature distribution at a point in a three layer system with none homogeneous boundary conditions. also, the effect of noisy data on final solution is studied. for solving this problem the general co...

In this paper, we present the numerical solution for the PDE-constrained optimization problem arises in cardiac electrophysiology. The monodomain model, which is a well-established model for simulating electrical behavior of the cardiac tissue, appears as the constraint in our problem. Our objective is to search for the optimal applied current, which is able to dampen out the excitation wavefro...

In this paper‎, ‎two extended three-term conjugate gradient methods based on the Liu-Storey ({tt LS})‎ ‎conjugate gradient method are presented to solve unconstrained optimization problems‎. ‎A remarkable property of the proposed methods is that the search direction always satisfies‎ ‎the sufficient descent condition independent of line search method‎, ‎based on eigenvalue analysis‎. ‎The globa...