طريقة تدرج مترافقة لحل مسائل الأمثليات غير المقيدة
Abstract
تم في هذا البحث تقديم طريقة عددية لحل مسألة الأمثليات غير المقيدة. تعتمد الطريقة على إنشاء قاعدة من المتجهات المترافقة، ثم تحديثها تكراريا بادخال متجهات تدرج مترافقة تحقق شرط الانحدار الأشد وشروط وولف-باول. اختُبِرتْ الطريقة بحل مجموعة من مسائل الاختبار القياسية الموجودة في دراسات سابقة. تبين النتائج العددية أن الطريقة المقترحة تستطيع إيجاد الحل العددي المضبوط من أجل الدوال التربيعية، وتستطيع أيضا تقديم حلول عددية عالية الدقة إذا كانت دالة الهدف فوق تربيعية. وبمقارنة النتائج التي تم التوصل إليها مع نتائج الطرائق الأخرى تظهر الكفاءة والفعالية التطبيقية للطريقة المقترحة.
In this paper, we present numerical method for solving unconstrained optimization problems. The method is based on a set of conjugate search directions, and then this set is updated repeatedly by generating new conjugate gradient directions so that steepest descent condition and Wolfe- Powell conditions are satisfied. The method is tested on set of standard problems. Numerical experiments show that the proposed method can find exact solution for quadratic functions, so it can find high accurate solution for over quadratic functions. Moreover, the comparisons with other available results illustrate the applicability and efficiency of the presented method.
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