This implements the Semismooth Newton Augmented Lagrangian (SSNAL) Algorithm for convex clustering as described in the paper: https://proceedings.mlr.press/v80/yuan18a.html

Status

The implementation now correctly follows the mathematical formulas from the paper. Recent fixes addressed critical bugs in the SSNCG subproblem solver that were preventing proper convergence.

Recent Fixes

The following mathematical bugs have been fixed:

1. Dual proximal operator scaling: The proxdual_pU function now correctly scales projection ball radii by the tau parameter (σ·w_ij).

2. Active-set handling in Hessian: The semismooth Newton Hessian approximation now correctly zeros out active-set columns, ensuring only inactive constraints contribute to the Newton direction.

Dependencies

• numpy
• scipy
• pylops

To Do

• Tests
• Examples
• Performance benchmarking