Gradient descent for Tikhonov functionals with sparsity constraints: theory and numerical comparison of step size rules

Pham Quy Muoi, Dirk A. Lorenz, Peter Maass

Publication date: 25 April 2014

Published in: ETNA. Electronic Transactions on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: http://www.emis.de/journals/ETNA/vol.39.2012/pp437-463.dir/pp437-463.html

zbMATH Keywords

convergence parameter identification step size control elliptic equation nonlinear inverse problems gradient descent sparsity constraints numerical comparison iterated soft shrinkage accelerated gradient method

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Inverse problems for PDEs (35R30) Nonlinear elliptic equations (35J60) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Numerical solutions to equations with nonlinear operators (65J15) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Numerical solution to inverse problems in abstract spaces (65J22)

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