Using a new type of formula conjugate on the gradient methods

Basim A. Hassan, Ranen M. Sulaiman


Unconstrained optimization problems, such as energy minimization, can be solved using the conjugate gradient method. For its major characteristic, the optimal formula conjugate encompasses all conjugate gradient algorithms. In conjugate gradient approaches, the formula conjugate is typically the focus point and it's playing a very important role for conjugate gradient approaches. To offer the essential descent criteria in this work, we devised a novel formula based on the second order Taylor which have the descent property too. Our research focused on our suggested method's-convergence property with Wolfe condition is established and numerical performance. Comparison to FR-method, the new algorithem shows significant improvement in numerical results.


Conjugate gradient; Convergence property; Descent property; Formula conjugate gradient; Numerical results;

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