AI 中文总结
本文针对谱面体上的光滑凸最小化问题，提出一种确定性、无参数的Frank-Wolfe型方法，消除了同类方法的严格互补性等局限，得到与环境维度无关的线性收敛速率。
AI 中文摘要
我们基于仅依赖极端特征向量计算的Frank-Wolfe型方法，研究谱面体上的光滑凸最小化问题。在近期工作\uc120[garber2026randomized]中，我们首次在二次增长条件下得到了与环境维度无关的线性收敛速率，但该方法存在额外的强严格互补性假设、具有随机性、线性速率仅在预烧阶段后以期望形式成立，且需要目标函数的光滑性常数。本文证明这些局限可被消除：假设二次增长条件及所有最优解具有相同秩，且不做严格互补性假设，我们提出一种确定性、无参数的Frank-Wolfe型方法，其全局收敛速率与环境维度无关且为线性。
英文摘要
We consider smooth convex minimization over the spectrahedron using Frank-Wolfe-type methods based only on extreme-eigenvector computations. In our recent work \cite{garber2026randomized} we presented the first ambient-dimension-independent linear convergence rate under quadratic growth. However, the method makes an additional strong strict complementarity assumption, it is randomized, its linear rate holds only after a burn-in phase and in expectation, and it requires the objective smoothness constant. We show that these limitations can be removed. Assuming quadratic growth and that all optimal solutions have the same rank, but without assuming strict complementarity, we give a deterministic and parameter-free Frank-Wolfe-type method with a global ambient-dimension-independent linear convergence rate.
