Uniqueness of OGM in smooth convex minimization

Determine whether the Optimized Gradient Method (OGM) is the uniquely minimax optimal deterministic first-order algorithm for smooth convex minimization using the gradient oracle, i.e., ascertain if any other deterministic first-order method achieves the exact optimal worst-case rate on this problem class.

Background

The paper discusses exact optimal algorithms for various optimization classes, noting that for smooth convex minimization OGM achieves exact optimality. However, while exact optimality is known, the authors explicitly state that the uniqueness of OGM among deterministic first-order gradient methods remains unknown.

This uncertainty is highlighted alongside similar questions for strongly convex minimization (ITEM) and composite minimization (OptISTA), motivating a broader investigation into uniqueness beyond the fixed-point setting characterized in the paper.