Smooth realization of Yuan’s fixed trajectory

Determine whether the particular fixed trajectory constructed by Yuan for exact-line-search variable-metric methods admits a realization by a continuously differentiable-to-all-orders (C^\infty) objective.

Background

Yuan’s construction established that the infimum of possible adjacent-iterate Q-orders is one for uniformly convex C^2 objectives, using examples with Q-order 1+1/N. The paper distinguishes that family from the question of whether the specific trajectory arising in Yuan’s construction can be realized by an objective that is smooth to all orders. The present paper does not resolve this trajectory-specific realization problem; instead, it uses a different construction to attain Q-order one on a globally C^\infty strongly convex objective.