An alternative extrapolation scheme of PDHGM for saddle point problem with nonlinear function

Gao, Ying; Zhang, Wenxing

doi:10.1007/s10589-023-00453-8

Cited by 4 publications

(2 citation statements)

References 40 publications

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“…for solving linear SPP, which significantly boosts the numerical efficiency of PDHG. In this paper, pursuing the tracks of the nonlinear analysis in [52,58] and the relaxed step lengths criterion (21), we shall develop a variant PDHG for solving nonlinear SPP. Let us define…”

Section: Solver For Parametric Bd Model (17)mentioning

confidence: 99%

Generalized variational framework with minimax optimization for parametric blind deconvolution

Cao,

Han,

Wang

et al. 2024

Inverse Problems

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Blind deconvolution (BD), which aims to separate unknown colvolved signals, is a fundamental problem in signal processing. Due to the ill-posedness and underdetermination of the convolution system, it is a challenging nonlinear inverse problem. This paper is devoted to the algorithmic studies of parametric BD, which is typically applied to recover images from ad hoc optical modalities. We propose a generalized variational framework for parametric BD with various priors and potential functions. By using the conjugate theory in convex analysis, the framework can be cast into a nonlinear saddle point problem. We employ the recent advances in minimax optimization to solve the parametric BD by the nonlinear primal-dual hybrid gradient method, with all subproblems admitting closed-form solutions. Numerical simulations on synthetic and real datasets demonstrate the compelling performance of the minimax optimization approach for solving parametric BD.

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Section: Solver For Parametric Bd Model (17)mentioning

confidence: 99%

Generalized variational framework with minimax optimization for parametric blind deconvolution

Cao,

Han,

Wang

et al. 2024

Inverse Problems

Self Cite

View full text Add to dashboard Cite

show abstract

“…The (local) convergence analysis of the above algorithm to a solution of ( 23)-( 24) is rather involved and can be found under various technical assumptions 16 in Valkonen ( 2014), and more recently in Valkonen (2023). Theorem 1 in Gao and Zhang (2023) gives a shorter proof of local convergence (for a slightly different algorithm where the linearization of the nonlinear map Λ is used at the level of the updates (30) for v instead of the updates (28) for y).…”

Section: Proximal Primal-dual Algorithm In the General Casementioning

confidence: 99%