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Register a new userOn min/max problems by using Moreau-Yosida with tow variables
دراسة لمسائل القيم الصغرى / العظمى باستخدام دالة مورو ـــــ يوشيدا بمتحولين
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Tishreen University ورقة بحثية
Publication date
2016
fields
Mathematics
and research's language is
العربية
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Shamra Editor
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قمنا في هذا البحث بدراسة بعضاً من الخواص الأساسية لدالة موروـــــ يوشيدا بمتحولين ، و تعميم بعض النتائج المتعلقة بدراسة التقارب لمتتالية من الدوال المحدبة ـــــــ المقعرة و متتالية دوال موروـــــ يوشيدا الموافقة لها ، و المبرهنة الأساسية التي حصلنا عليها إنه من أجل أي متتالية من الدوال المحدبة ـــــ المقعرة إذا كانت متقاربة بالنسبة لمسافة موروـــــ يوشيدا ، فإن متتالية دوال موروـــــ يوشيدا الموافقة لها تكون متقاربة وفق مفهوم موسكو ـــــ فوق/تحت البيان .
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 corresponding , 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 .
References used
ATTOUCH, H. :Variational convergence for functions and operators . Pitman, London, 1984 , 120-264
ATTOUCH, H; WETS,R.: Convergence Theory of saddle functions .Trans. Amaer. Math.Soc. 280, n (1), 1983 , 1-41
ATTOUCH, H ; AZE, D. ; WETS,R. :On continuity properties of the partial Legendre- FenchelTrasform : Convergence of sequences augmented Lagrangianfunctions , Moreau- Yoshida approximates and subdiffferential operators . FERMAT Days 85: Mathematics for Optimization, 1986
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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 s
tudy properties of generalized approximation and prove equivalence between epigraph – convergence and pointwise convergence of the generalized Moreau – Yosida Approximation.
In this paper, we develop spline collocation technique for the numerical solution of
general twelfth-order linear boundary value problems (BVPs). This technique based on
polynomial splines from order sixteenth as well as five collocation points at
every
subinterval of BVPs. The method developed not only approximates the solution of BVP,
but its higher order derivatives as well. We show that the spline collocation method is
existent and unique when it is applied into a test problem. Also, its global truncation error
is estimated. Moreover, the purposed spline method when applied to test problems will be
consistent and convergent from sixteenth order. Three numerical examples are given to
illustrate the applicability and efficiency of the new method. Comparisons of our results
with some other methods show that our method is very effective and successful.
In this paper, the numerical solution of general linear fifth-order boundary-value problem (BVP) is considered. This problem is transformed into three initial value problems (IVPs) and then spline functions with four collocation points are applied to
the three IVPs. The presented spline method enables us to find the spline solution and derivatives up to fifth-order of BVP. By giving four examples and comparing with the other methods, the efficiency and highly accurate of the method will be shown.
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
function on Banach space. Proved equivalence between Mosco-epi-convergence of
sequence functions and pointwise convergence of Moreau-Bregman envelope We
also studied the strong and weak convergence of resolvent operators According to
the concept of Bregman distance.
In this research we will find a law of the large numbers for random convex – concave closed functions, and generalize some results related to lower semi- continuous functions to similar results concerning the convex– concave functions, and that will
be done with using the parent convex functions and the Mosco-epi \ hypo-convergence.
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