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Register a new userGeneralized Moreau – Yosida Approximation
دراسة تقريب مورو ـ يوشيدا المعمّم
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يهدف البحث إلى الاستفادة من مسافة برغمان و دالة برغمان للحصول على الدالة التقريبية المعدّلة التي تلعب دوراً هاماً في علم الأمثليات, حيث نقوم باستبدال الشكل التربيعي بتقريب مورو يوشيدا بمسافة برغمان و دراسة خواص دالة التقريب المعممة بمقارنتها بتقريب دالة مورو يوشيدا و من ثمّ برهان التكافؤ بين التقارب فوق البياني لمتتالية من الدوال و التقارب البسيط لمتتالية الدوال التقريبية المعدّلة الموافقة لهذه الدوال.
The purpose of the research is to study the Bergman function and Bergman distance to generalize Moreau – Yosida Approximation. To do that we replace the quadratic additive terms in Moreau – Yosida Approximates by more general Bergman distance and study properties of generalized approximation and prove equivalence between epigraph – convergence and pointwise convergence of the generalized Moreau – Yosida Approximation.
References used
Attouch, H. Variational Convergence For Functions And Operators .Pitman, London, 1984 , 120-264
Attouch, H.; Aze, D.; Wets,R.On Continuity Properties Of The Partial Legendre- Fenchel Transform : Convergence Of Sequences Augmented Lagrangian Functions , Moreau-Yoshida Approximates And Subdiffferential Operators. Fermat Days 85: Mathematics For Optimization, 1986
Bauschke, H. H.; Combettes, P. L. Iterating Bregman Retractions, Siam Journal On Control And Optimization, Vol. 42, 596–636, 2003
Bauschke, H. H.; Borwein, J. M.; Combettes, P. L. Bregman Monotone Optimization Algorithms. Siam Journal On Control And Optimization, Vol. 42, 596–636, 2003
Bauschke, H. H.; Borwein, J. M. , Legendre Functions And The Method Of Random Bregman Projection, J. Convex Anal. 4 (1997), 27–67
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In this paper we study some basic properties of the Moreau-Yosida function with two variables , and generalize the results of related to study of the convergence for sequence of convex-concave functions and the sequence of Moreau-Yosida function corr
esponding , and the basic theorem that we proved is : for any sequence of convex-concave functions , if they are convergent of the Moreau-Yosida distance then the sequence of Moreau-Yosida function corresponding will be convergent to the concept of Mosco-epi/hypo graph convergence .
It is often useful to replace a function with a sequence of smooth functions
approximating the given function to resolve minimizing optimization problems.
The most famous one is the Moreau envelope. Recently the function was organized
using the Br
egman distance h D . It is worth noting that Bregman distance h D is
not a distance in the usual sense of the term. In general, it is not symmetric and it
does not satisfy the triangle inequality
The purpose of the research is to study the convergence of the Moreau envelope
function and the related proximal mapping depends on Bregman Distance for a
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also studied the strong and weak convergence of resolvent operators According to
the concept of Bregman distance.
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Finally, this study is used for approximation of the class on group of wide curves.
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we also use an operator as a useful method in defining b
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interval writhen defined condition,
The operator is used in zero points of the Chebyshev polynomials
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