Implement partial prox

[dpo]

• ShiftedNormL0;
• ShiftedNormL1;
• RootNormLhalf;
• ShiftedRootNormLhalf;
• ShiftedRootNormLhalfBinf; (RootNormLhalfBinf partial prox + tests #93)
• ShiftedNormL0Box; (use general boxes instead of trust regions #87)
• ShiftedNormL1Box; (use general boxes instead of trust regions #87)
• NuclearNorm;
• ShiftedNuclearNorm;
• Rank;
• ShiftedRank;
• cappedL1;
• ShiftedCappedL1;
• ShiftedIndBallL0;
• ShiftedIndBallL0Binf;

[MohamedLaghdafHABIBOULLAH]

Could you elaborate more on what is it the difference between the prox and the partial prox ?

[dpo]

The partial prox is the prox applied to a subset of variables. For example, the regularizer may be the $\ell_1$-norm of a subvector of $x$.