Extension of anchor-induced minimizer selection beyond affine solution sets

Determine whether the anchor-induced selection principle for the accelerated gradient flow with an endogenous gradient-memory anchor extends to objective functions whose nonempty solution sets are not affine.

Background

The paper proves that, when the solution set S=argmin F is a nonempty affine subspace and gamma>0, the primal trajectory converges to the Euclidean projection P_S(z_0) of the initial anchor onto S. The proof relies on conservation of the anchor component along directions parallel to the affine solution set.

The conclusion explicitly leaves unresolved whether an analogous selection principle holds for more general, non-affine solution sets.