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Register a new userGeneralized Lasry – Lions regularization function using Bregman distant
تعميم دالة تنظيم Lasry – Lions باستخدام مسافة بريغمان
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Tishreen University ورقة بحثية
Publication date
2014
fields
Mathematics
and research's language is
العربية
Authors
يمار حموي( باحث )
Created by
Shamra Editor
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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.
References used
ATTOUCH, H.: Variational convergence for functions and operators , Pitman,London ( 1984), 120-264
ATTOUCH, H.; AZE, D.: Approximation and regularization of arbitrary functions in Hilbert space by the Lasry-Lions method, Ann. Inst. Henri Poincare 10(3) (1993), pp. 289–312
BAUSCHKE, H. H. ; BORWEIN,J.M. : Legendre functions and the method of random Bregman projections .Journal of Convex Analysis 4 (1997) 27-67
BAUSCHKE, H. H. ; BORWEIN, J. M. ; COMBETTES, P. L. :Bregman monotone optimization Algorithms, SIAM J. Control Optim, vol. 42, pp. 596–636, 2003
BAUSCHKE, H. H., COMBETTES, P. L , NOLL, D.: Joint minimization with alternating Bregman proximity operators, Pacific J. Optim. 2 (2006), 401–424
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