From: A primal-dual fixed point algorithm for minimization of the sum of three convex separable functions
 | Condat ( \(\boldsymbol{\rho_{k}=1}\) ) | PDFP |
---|---|---|
Form | \(\overline{v}^{k+1}=\operatorname{prox}_{\sigma {f_{2}^{*}}}(\sigma Bx^{k}+\overline{v}^{k})\), \(x^{k+1}=\operatorname{prox}_{{\tau}{f_{3}}}(x^{k}-\tau \nabla {f_{1}}(x^{k})-{\tau} B^{T} (2\overline{v}^{k+1}-\overline{v}^{k}))\) | \(y^{k+1}=\operatorname{prox}_{{\gamma}{f_{3}}}(x^{k}-\gamma \nabla{f_{1}}(x^{k})-{\gamma} B^{T} \overline{v}^{k})\), \(\overline{v}^{k+1}=\operatorname{prox}_{\frac{\lambda }{\gamma }{f_{2}^{*}}}(\frac{\lambda}{\gamma}By^{k+1}+\overline{v}^{k})\), \(x^{k+1}=\operatorname{prox}_{{\gamma}{f_{3}}}(x^{k}-\gamma \nabla {f_{1}}(x^{k})-{\gamma} B^{T} \overline{v}^{k+1})\) |
\(f_{1}\neq0\) | \(\sigma\tau\lambda_{\mathrm{max} }(BB^{T})+\tau/(2\beta)\leq1\) | \(0<\lambda< 1/\lambda _{\mathrm{max}}(BB^{T})\), 0<γ<2β |
\(f_{1}=0\) | \(0<\sigma\tau\leq1/\lambda_{\mathrm{max} }(BB^{T})\) | \(0<\lambda< 1/\lambda_{\mathrm{max}}(BB^{T})\), 0<γ< + ∞ |
Relation | σ = λ/γ, τ = γ |