معلمة طيفية فعالة لتسريع خوارزمية التدرج المترافق
DOI:
https://doi.org/10.54153/sjpas.2025.v7i1.987الكلمات المفتاحية:
Conjugate gradient algorithms, Strong Wolfe Conditions, Numerical analysis, Spectral conjugate gradient, Inexact line searchالملخص
تشتهر أساليب التدرج المترافق (CG) بسرعتها وكفاءة الذاكرة في تحسين المشكلات. ومع ذلك، فإنّ بعض تركيبات طريقة CG التي تقوم بالتبديل بين معلمات CG المختلفة غالبًا ما تفوت القيم التي كان من الممكن تضمينها. علاوة على ذلك، فإنّ إظهار خصائص النّسب الكافية في هذه الطرق يعتمد عادةً على استراتيجية تفترض إمكانية استبعاد قيم دالة محددة. يقدم هذا البحث خوارزمية CG (SCG) طيفية جديدة تجمع بين معامل التدرج الطيفي ومعامل التدرج المترافق. تتميز الطريقة المقترحة بميزة فريدة تتمثل في كونها قابلة للتطبيق على مشكلات التحسين غير المقيدة واسعة النطاق. تم عرض النتائج العددية الأولية باستخدام بحث خط وولف القوي لإثبات كفاءة الطريقة المقترحة.
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