New Feature: Feasibility Polishing

[Lhongpei]

Summary

This PR introduces an optional feasibility-polishing phase that can be run after the normal PDHG solve.

What is new

• Two new command-line flags
  --feasibility_polishing # enable the phase
  --eps_feas_polish_relative <tol> # relative tolerance (default 1e-6)

Two independent polishing loops
– Primal polish: solves a feasibility primal problem.
– Dual polish: solves an unconstrained dual feasibility problem.

If both primal polish and dual polish success, polished solutions will be saved.

Implementation details

• New solver states primal_feas_polish_state_t and dual_feas_polish_state_t that reuse the GPU buffers already allocated for the main solver.
• New kernels compute_primal_residual_kernel, compute_dual_residual_kernel, zero_finite_value_vectors_kernel and helper functions compute_primal_residual, compute_dual_residual.
• New termination reason TERMINATION_REASON_FEAS_POLISH_SUCCESS.

README

• Add new flags in the table of flags.
• Add a subsection to introduce this new feature.

[ZedongPeng]

Hi @Lhongpei, thank you for the PR! Please let us know once it’s ready for review.