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Generalized Lasry – Lions regularization function using Bregman distant

تعميم دالة تنظيم Lasry – Lions باستخدام مسافة بريغمان

1510   1   37   0 ( 0 )
 Publication date 2014
  fields Mathematics
and research's language is العربية
 Created by Shamra Editor




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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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