Nonmonotone Barzilai-Borwein gradient algorithm for \(\ell_1\)-regularized nonsmooth minimization in compressive sensing

DOI10.1007/s10915-013-9815-8zbMath1306.65216arXiv1207.4538OpenAlexW2067425611MaRDI QIDQ474971

Liqun Qi, Soon-Yi Wu, Yun-hai Xiao

Publication date: 25 November 2014

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1207.4538

zbMATH Keywords

nonsmooth optimizationiterationnumerical experimentsnonconvex optimizationnonmonotone line searchquasi-Newton methodglobally convergentcompressive sensinggradient algorithmHessian approximation\(\ell_1\) regularizationBarzilai-Borwein gradient algorithmpositive componentssmooth term

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Convex programming (90C25) Nonconvex programming, global optimization (90C26) Nonlinear programming (90C30)

Related Items (10)

Accelerating optimization by tracing valley ⋮ An approximate Newton-type proximal method using symmetric rank-one updating formula for minimizing the nonsmooth composite functions ⋮ A diagonally scaled Newton-type proximal method for minimization of the models with nonsmooth composite cost functions ⋮ Nonmonotone adaptive Barzilai-Borwein gradient algorithm for compressed sensing ⋮ A new generalized shrinkage conjugate gradient method for sparse recovery ⋮ Low-rank and sparse matrices fitting algorithm for low-rank representation ⋮ Alternating direction and Taylor expansion minimization algorithms for unconstrained nuclear norm optimization ⋮ A class of line search-type methods for nonsmooth convex regularized minimization ⋮ Exact Penalty Function for $\ell_{2,1}$ Norm Minimization over the Stiefel Manifold ⋮ Combining line search and trust-region methods forℓ1-minimization

Uses Software

• L-BFGS
• CUTEr
• NESTA
• SPGL1
• FPC_AS
• TwIST

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