Study the Convergence of Moreau – Bregman Envelope in Reflexive Banach Spaces.

Authors

  • Mohamed Soueycatt
  • Yara Mohammad
  • Yamar Hamwi

Abstract

 

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 Bregman distance   . It is worth noting that Bregman distance  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.

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Published

2018-11-14

How to Cite

1.
Soueycatt M, Mohammad Y, Hamwi Y. Study the Convergence of Moreau – Bregman Envelope in Reflexive Banach Spaces. TUJ-BA [Internet]. 2018Nov.14 [cited 2024Nov.24];40(5). Available from: https://journal.tishreen.edu.sy/index.php/bassnc/article/view/4645

Issue

Vol. 40 No. 5 (2018): العلوم الأساسية

Section

Articles

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