In this paper, we study first-order algorithms for solving fully composite optimization problems over bounded sets. We treat the differentiable and non-differentiable parts of the objective separately, linearizing only the smooth components. This provides us with new generalizations of the classical and accelerated Frank-Wolfe methods, that are applicable to non-differentiable problems whenever we can access the structure of the objective. We prove global complexity bounds for our algorithms that are optimal in several settings.

翻译：本文研究在有界集上求解全复合优化问题的一阶算法。我们将目标函数的可微部分与不可微部分分开处理，仅对光滑分量进行线性化。这为我们提供了经典及加速Frank-Wolfe方法的新推广，使其能够应用于可访问目标结构的非可微问题。我们证明了算法在多种场景下具有最优的全局复杂度界。