التحليل الرياضي لخرائط الثبات P لتحسين المتجهات المخروطية البارامترية
خلاصة
يتعامل تحليل الاستقرار لأنظمة البرمجة غير الخطية مع التغييرات المحتملة لمعلمات النظام و/أو المعادلات التي تحافظ على استقرار الحلول. من المتطلبات الحاسمة دراسة النظام غير الخطي وقيمه العملية، وتحديدًا التأثير الاقتصادي في معظم تطبيقات العالم الحقيقي. يعرض هذا البحث بعض النتائج فيما يتعلق بتحليل الاستقرار المطابق لمشاكل تحسين المتجهات المخروطية البارامترية. بالنسبة لمشكلات التحسين الأخيرة هذه، يتم النظر في نوعين جديدين من خرائط P-Stability، وهما خريطة مفاهيم P-Stability وخريطة اضطراب P-Stability، استنادًا إلى ستة أنواع من المجموعات: مجموعة P-feasible، ومجموعة P-solvability، يتم تحديد الأنواع الأول والثاني والثالث والرابع من مفاهيم P-Stability فيما يتعلق بمخروط هيمنة محدد P. علاوة على ذلك، تم توفير وإثبات الخصائص النوعية لخرائط P-Stability في ظل بعض افتراضات الاستمرارية والتحدب على الوظيفة الموضوعية. على وجه التحديد، يتم التحقيق في الاتصالات بين خرائط P-Stability ومجموعة فكرة P-Stability. وبناء على ذلك، تم توسيع هذه الخصائص لتشمل خرائط الاضطراب P. بالإضافة إلى ذلك، تم استخدام فكرة P-stability بشكل كبير في تطبيقات مختلفة مثل خصوصية الشبكة والمجالات الهندسية وبعض النماذج المالية للأعمال.
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