Smart initialization of dual variable

When using the dual variable for gradient descent, we usually set its initial value as ```np.zeros(p-1)```, including the algorithm of ADMM, Chambolle-Pock, CondatVu and Dual Proximal GD. Maybe there is a smarter start for dual variable.

Start by reviewing the ADMM, Chambolle-Pock, CondatVu, and Dual Proximal GD implementations and their current np.zeros(p-1) dual-variable initialization. Define what a smarter initialization should achieve, then validate the proposed approach across the named algorithms and compare it with the existing initialization.

Written by the indexing model from the issue text.