The hybrid conjugate gradient (CG) method is among the efficient variants of CG method for solving optimization problems. This is due to their low memory requirements and nice convergence properties. In this paper, we present an efficient hybrid CG method for solving unconstrained optimization models and show that the method satisfies the sufficient descent condition. The global convergence prove of the proposed method would be established under inexact line search. Application of the proposed method to the famous statistical regression model describing the global outbreak of the novel COVID-19 is presented. The study parameterized the model using the weekly increase/decrease of recorded cases from December 30, 2019 to March 30, 2020. Preliminary numerical results on some unconstrained optimization problems show that the proposed method is efficient and promising. Furthermore, the proposed method produced a good regression equation for COVID-19 confirmed cases globally.

We consider a class of invariant Hyperbolic scaling of a strictly convex quadratic function, to extend the family of the conjugate gradient methods for solving unconstrained minimization problems. An algorithm is derived and evaluated numerically. The results indicate that, in general, the new algorithm is superior to the classical standard CG-algorithm. Keywords: A Hyperbolic Rational Model, Conjugate gradient methods. ‫ا‬ ‫الزائدية‬ ‫النموذج‬‫لنسبية‬ ‫المقيدة‬ ‫غير‬ ‫الخطية‬ ‫غير‬ ‫لالمثلية‬ ‫حسن‬ ‫عباس‬ ‫باسم‬ ‫االسدي‬ ‫حسين‬ ‫نضال‬ ‫ياضيات‬ ‫الر‬ ‫و‬ ‫الحاسبات‬ ‫علوم‬ ‫كلية‬ ، ‫الموصل‬ ‫جامعة‬ ‫البحث:‬ ‫استالم‬ ‫تاريخ‬ 7 / 9 / 2003 ‫البحث:‬ ‫قبول‬ ‫تاريخ‬ 16 / 12 / 2003 ‫الملخص‬ ‫ال‬ ‫النموذج‬ ‫من‬ ‫عمومية‬ ‫اكثر‬ ‫نموذج‬ ‫بناء‬ ‫تم‬ ‫البحث‬ ‫هذا‬ ‫في‬ ‫المشروطة‬ ‫غير‬ ‫لألمثلية‬ ‫بيعي‬ ‫تر‬ ‫ةة‬ ‫بييي‬ ‫التر‬ ‫ةة‬ ‫للدال‬ ‫الثابت‬ ‫المقياس‬ ‫ذات‬ ‫األصناف‬ ‫أحد‬ ‫النوع‬ ‫هذا‬ ‫ويعتبر‬ ‫ائد‬ ‫الز‬ ‫القطع‬ ‫يمثل‬ ‫النموذج‬ ‫وهذا‬ ‫ةروطة‬ ‫المش‬ ‫ةر‬ ‫غي‬ ‫ةة‬ ‫مثلي‬ ‫ا‬ ‫ةائل‬ ‫ما‬ ‫ةل‬ ‫ح‬ ‫ةي‬ ‫ف‬ ‫ةة‬ ‫افق‬ ‫المتر‬ ‫ةات‬ ‫المتها‬ ‫ةر‬ ‫ط‬ ‫وتطوير‬ ‫توسيع‬ ‫لغرض‬ . ‫المحددة‬ ‫الن‬ ‫ان‬ ‫و‬ . ‫ةدديا‬ ‫ع‬ ‫ةت‬ ‫وميم‬ ‫ةدة‬ ‫جدد‬ ‫ةة‬ ‫ارزمي‬ ‫خو‬ ‫اشتقا‬ ‫تم‬ ‫ةة‬ ‫ارزمي‬ ‫اليو‬ ‫أن‬ ‫ةت‬ ‫أأبت‬ ‫ةا‬ ‫أليا‬ ‫ةل‬ ‫التوص‬ ‫ةم‬ ‫ت‬ ‫ةي‬ ‫الت‬ ‫ةائ‬ ‫ت‬ . ‫المهال‬ ‫هذا‬ ‫في‬ ‫فة‬ ‫المعر‬ ‫القياسية‬ ‫ارزمية‬ ‫اليو‬ ‫من‬ ‫كفاءة‬ ‫اكثر‬ ‫هي‬ ‫الهدددة‬ : ‫المفتاحية‬ ‫الكلمات‬ ‫النسبية‬ ‫الزائدية‬ ‫النموذج‬ ‫افق.‬ ‫المتر‬ ‫التدرج‬ ‫ائق‬ ‫طر‬ ,

In this paper, a modified globally convergent self-scaling BFGS algorithm for solving convex unconstrained optimization problems was investigated in which it employs exact line search strategy and the inverse Hessian matrix approximations were positive definite. Experimental results indicate that the new proposed algorithm was more efficient than the standard BFGS-algorithm.

<span><span>Quasi-Newton methods are a class of numerical methods for </span>solving the problem of unconstrained optimization. To improve the overall efficiency of resulting algorithms, we use the quasi-Newton methods which is interesting for quasi-Newton equation. In this manuscript, we present a modified BFGS update formula based on the new quasi-Newton equation, which give a new search direction for solving unconstrained optimizations proplems. We analyse the convergence rate of quasi-Newton method under some mild condition. Numerical experiments are conducted to demonstrate the efficiency of new methods using some test problems. The results indicates that the proposed method is competitive compared to the BFGS methods as it yielded fewer iteration and fewer function evaluations.</span>

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