Descent gradient methods for nonsmooth minimization problems in ill-posed problems

DOI10.1016/j.cam.2015.11.039zbMath1332.65072OpenAlexW2201242825MaRDI QIDQ908377

Pham Quy Muoi, Dinh Nho Hào, Peter Maass, Michael K. Pidcock

Publication date: 4 February 2016

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2015.11.039

zbMATH Keywords

Hilbert spacenonlinear inverse problemstotal variation regularizationsparsity regularizationparameter identification problemdescent gradient methodNesterov's accelerated algorithmnonnegative sparse regularization

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Nonlinear elliptic equations (35J60) Nonlinear ill-posed problems (47J06) Numerical solutions to equations with nonlinear operators (65J15) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Numerical solution to inverse problems in abstract spaces (65J22)

Related Items (5)

Convergence of proximal algorithms with stepsize controls for non-linear inverse problems and application to sparse non-negative matrix factorization ⋮ Proximal algorithm for minimization problems in \(l_0\)-regularization for nonlinear inverse problems ⋮ Inverse problems with nonnegative and sparse solutions: algorithms and application to the phase retrieval problem ⋮ Orthogonal intrinsic mode functions via optimization approach ⋮ \(l^1\)-weighted regularization for the problem of recovering sparse initial conditions in parabolic equations from final measurements

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