Algorithm 4 ONMFTV-PALM

1:Input$X\in {\mathbb{R}}_{\ge 0}^{M\times N},K\in \mathbb{N},{\sigma }_1,{\sigma }_2,\tau >0,i=0$ 2:Initialize$U^{\left[0\right]},W^{\left[0\right]}\in {\mathbb{R}}_{\ge 0}^{M\times K},V^{\left[0\right]}\in {\mathbb{R}}_{\ge 0}^{K\times N}$ 3:repeat 4:${\displaystyle {\eta }_{U^{\left[i\right]}}=P_{\mathrm{OWER}}{I}_{T_U}(V^{\left[i\right]},W^{\left[i\right]})}$ 5:${\displaystyle U^{[i+1]}={\left. [{prox}_{\tau {\eta }_{U^{\left[i\right]}}\mathcal{J}}\left(U^{\left[i\right]}-{\eta }_{U^{\left[i\right]}}{\nabla }_U\mathcal{F}(U^{\left[i\right]},V^{\left[i\right]},W^{\left[i\right]})\right)\right]}_{\ge 0}}$ 6:${\displaystyle {\eta }_{V^{\left[i\right]}}=P_{\mathrm{OWER}}{I}_{T_V}\left(U^{[i+1]}\right)}$ 7:${\displaystyle V^{[i+1]}={\left. [V^{\left[i\right]}-{\eta }_{V^{\left[i\right]}}{\nabla }_V\mathcal{F}(U^{[i+1]},V^{\left[i\right]},W^{\left[i\right]})\right]}_{\ge 0}}$ 8:${\displaystyle {\eta }_{W^{\left[i\right]}}=P_{\mathrm{OWER}}{I}_{T_W}\left(U^{[i+1]}\right)}$ 9:${\displaystyle W^{[i+1]}={\left. [W^{\left[i\right]}-{\eta }_{W^{\left[i\right]}}{\nabla }_W\mathcal{F}(U^{[i+1]},V^{[i+1]},W^{\left[i\right]})\right]}_{\ge 0}}$ 10:${\displaystyle i\leftarrow i+1}$ 11:untilStopping criterion satisfied