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Merging Multigrid Optimization with SESOP [article]

Tao Hong, Irad Yavneh, Michael Zibulevsky
2021 arXiv   pre-print
A merger of two optimization frameworks is introduced: SEquential Subspace OPtimization (SESOP) with MultiGrid (MG) optimization.  ...  We then study the asymptotic convergence factor of the two-level version of SESOP-MG (dubbed SESOP-TG) for optimization of quadratic functions, and derive approximately optimal fixed parameters, which  ...  We analyze the convergence rate of SESOP-TG via local Fourier analysis (LFA) [2, 14] for quadratic optimization problems, and thus quantify the acceleration due to SESOP by means of the so-called h-ellipticity  ... 
arXiv:1812.06896v4 fatcat:natlksu7r5awbl2dienmqfcoge

Speeding-Up Convergence via Sequential Subspace Optimization: Current State and Future Directions [article]

Michael Zibulevsky
2013 arXiv   pre-print
In recent years we introduced a general framework for large-scale unconstrained optimization -- Sequential Subspace Optimization (SESOP) and demonstrated its usefulness for sparsity-based signal/image  ...  multiplication by Hessian is available; Stochastic optimization methods - for problems with large stochastic-type data; Multigrid methods - for problems with nested multilevel structure.  ...  This should provide best combination of SESOP and multigrid advantages, because fine-grid iterations have no break, and CG-type acceleration properties are preserved.  ... 
arXiv:1401.0159v1 fatcat:j4pysvjrqjfz7ozapzxpn7tj4a

Efficient Beltrami Image Filtering via Vector Extrapolation Methods

Guy Rosman, Lorina Dascal, Avram Sidi, Ron Kimmel
2009 SIAM Journal of Imaging Sciences  
The Beltrami flow is also strongly linked * EFFICIENT BELTRAMI IMAGE FILTERING VIA VECTOR EXTRAPOLATION 859 to similar diffusion processes defined on nonflat manifolds [41] , and formulations of it were  ...  In this paper, we propose using vector extrapolation techniques for accelerating the convergence of the explicit schemes for the Beltrami flow.  ...  Another method which exploits previous descent directions in order to efficiently minimize a cost function is the sequential subspace optimization (SESOP) [15] method.  ... 
doi:10.1137/080728391 fatcat:tjvq3pizdzcrdpxi5wu7lkn2nq