Convergence of proximal algorithms with stepsize controls for non-linear inverse problems and application to sparse non-negative matrix factorization

DOI10.1007/s11075-019-00864-xzbMath1455.65091OpenAlexW3010081100MaRDI QIDQ827076

Dinh Nho Hào, Quy Muoi Pham, Delf Lachmund

Publication date: 6 January 2021

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-019-00864-x

zbMATH Keywords

sparse matrix factorizationnon-smooth optimizationsparsity regularizationalternating proximal iterationnon-linear inverse problems

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Numerical mathematical programming methods (65K05) Nonsmooth analysis (49J52) Numerical methods based on nonlinear programming (49M37) Numerical solution to inverse problems in abstract spaces (65J22)

Related Items (2)

Off-diagonal symmetric nonnegative matrix factorization ⋮ Existence of optimal solution to the problem of finding an initial condition for nonlinear diffusion from integral observations

Cites Work

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• Multi-penalty regularization in learning theory
• Multi-parameter Tikhonov regularization
• Proximal alternating linearized minimization for nonconvex and nonsmooth problems
• Convergence rates for total variation regularization of coefficient identification problems in elliptic equations. II
• Descent gradient methods for nonsmooth minimization problems in ill-posed problems
• Algorithms and applications for approximate nonnegative matrix factorization
• Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward-backward splitting, and regularized Gauss-Seidel methods
• Distributed learning with multi-penalty regularization
• Gradient descent for Tikhonov functionals with sparsity constraints: theory and numerical comparison of step size rules
• Sparsity-enforcing regularisation and ISTA revisited
• Multi-parameter Tikhonov regularization with the ℓ ⁰ sparsity constraint
• Semismooth Newton and quasi-Newton methods in weighted ℓ¹-regularization
• A Block Coordinate Descent Method for Regularized Multiconvex Optimization with Applications to Nonnegative Tensor Factorization and Completion
• Convergence rates for total variation regularization of coefficient identification problems in elliptic equations I
• Reconstructing conductivity coefficients based on sparsity regularization and measured data in electrical impedance tomography
• Convergence rates for Tikhonov regularisation of non-linear ill-posed problems
• Convergence rates and source conditions for Tikhonov regularization with sparsity constraints
• Inverse problems with nonnegative and sparse solutions: algorithms and application to the phase retrieval problem
• An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
• Learning the parts of objects by non-negative matrix factorization
• Proximité et dualité dans un espace hilbertien

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