تعميم دالة تنظيم Lasry – Lions باستخدام مسافة بريغمان
Abstract
يهدف هذا البحث إلى الاستفادة من مسافة بريغمان لتعميم دالة تنظيم Lasry – Lions التي تلعب دوراً هاماً في علم الأمثليات, وذلك باستبدال الشكل التربيعي بمسافة بريغمان ( مسافة غير مترية), وتمّت دراسة بعض خواص هذه الدّالة حيثُ تمً البرهان على إنّها مستمرة, وأنّ مجموعة حلول مسألة الأمثليات تتطابق مع مجموعة الحلول الصغرى لدالة التنظيم المعمّمة.
The purpose of the research is to study Bergman distance to generalize Lasry – Lions regularization which play important role of theory optimization.
To do that we replace the quardatic additive terms in Lasry – Lions regularization by more general Bergman distance (non metric distance), and study properties generalized approximation and proof its continuous as we give a relationship between the solution minimization sets of function and Lions – Lasry Regularization and others properties.
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