On second-order epi-derivative in terms of ρ-hausdorff distance
Author
Source
Mu'tah Journal for Research and Studies : Natural and Applied Sciences Series
Issue
Vol. 26, Issue 1 (31 Dec. 2011), pp.23-42, 20 p.
Publisher
Mutah University Deanship of Academic Research
Publication Date
2011-12-31
Country of Publication
Jordan
No. of Pages
20
Main Subjects
Topics
Abstract AR
تلعب المشتقات فوق البيانية من المرتبة الثانية دورا هاما في التحليل غير المنتظم و في تحيد الأمثليات.
باستخدام مسافة –p هاوسدورف, كمفهوم لتقارب المجموعات, و بمطابقة الدوال مع فوق بياناتها و مؤشرات التفاضلات الجزئية مع بياناتها نحصل على بعض العلاقات الجديدة بين المشتق فوق البياني من المرتبة لدالة محدبة و المشتق البياني لمؤشر التفاضل الجزئي.
و نبرهن أيضا أن مرافق المشتق فوق البياني من المرتبة لدالة محدبة يطابق المشتق فوق البياني من المرتبة الثانية لمرافق هذه الدالة.
هذه النتائج هي تعميم لنتائج تعود للرياضي روكافولار في فضاءات منتهية البعد.
Abstract EN
The second-order epi-derivatives plays an important role in nonsmooth analysis and in statements of optimality conditions.
Identifying functions with their epigraphs and subdifferentials operators with their graphs and using, as set convergence notion, the −Hausdorff distance convergence, we obtain in Banach spaces, some new relations between the second-order epi-derivative of convex function and proto-derivative of subdifferential operator, one also proves that the conjugate of second-order epi-derivative of convex function is the second-order epi-derivative of its conjugate function.
These results are extended of results introduced by Rockafellar in finite-dimensioal spaces.
American Psychological Association (APA)
suiqat, Muhammad Yusuf. 2011. On second-order epi-derivative in terms of ρ-hausdorff distance. Mu'tah Journal for Research and Studies : Natural and Applied Sciences Series،Vol. 26, no. 1, pp.23-42.
https://search.emarefa.net/detail/BIM-320696
Modern Language Association (MLA)
suiqat, Muhammad Yusuf. On second-order epi-derivative in terms of ρ-hausdorff distance. Mu'tah Journal for Research and Studies : Natural and Applied Sciences Series Vol. 26, no. 1 (2011), pp.23-42.
https://search.emarefa.net/detail/BIM-320696
American Medical Association (AMA)
suiqat, Muhammad Yusuf. On second-order epi-derivative in terms of ρ-hausdorff distance. Mu'tah Journal for Research and Studies : Natural and Applied Sciences Series. 2011. Vol. 26, no. 1, pp.23-42.
https://search.emarefa.net/detail/BIM-320696
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references : p. 41-42
Record ID
BIM-320696