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:在本文中,我们研究一阶算法,以解决被捆绑的组合性优化问题。我们将目标的不同和无区别的部分分开处理,只将光滑的组件线化。这为我们提供了传统和加速的弗兰克-沃夫方法的新的概括性,只要我们能够进入目标的结构,这些方法就适用于无区别的问题。我们证明,对于几种情况下最理想的我们算法来说,我们的方法具有全球性的复杂性界限。</s>