دراسة استقرارية النقاط السرجية لمسائل القيم القصوى لدوال محدبة/ مقعرة
Abstract
الهدف من البحث هو دراسة استقرار النقاط السرجية لمسائل القيم القصوى لدوال محدبة / مقعرة حيث نقوم في هذا البحث بتعميم بعض النتائج المتعلقة بالدوال المحدبة (المقعرة) ذات المتحول الواحد والتي درست من قبل أتوش و ويتس إلى دوال محدبة / مقعرة بمتحولين ودراسة العمليات الجبرية فوق/ تحت- البيانية وذلك بتحويل المسألة إلى مسألتين (مسألة قيم صغرى ومسألة قيم عظمى) وهذا يتم باستخدام الدوال الحدية الدنيا والعليا لدالة محدبة / مقعرة .
The purpose of the research is to study the stability of thesaddle points of min\max problems of convex \ concave functions . In this research we will generalize some results related to convex (concave) functions which have been studied by Attouch and Wits to convex \ concave functions , besides to studying the epi\hypo graphical algebraic operations , for that we will divide the problem into two problems (min problem and max problem) and that will be done with using the upper marginal function and lower marginal function of convex \ concave function .
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