Universal Conditional Gradient Sliding for Convex Optimization скачать в хорошем качестве

Universal Conditional Gradient Sliding for Convex Optimization

We present a first-order projection-free method, namely, the universal conditional gradient sliding (UCGS) method, for solving approximate solutions to convex differentiable optimization problems. For objective functions with Lipschitz continuous gradients, we show that UCGS is able to terminate with approximate solutions and its complexity for gradient evaluations and linear objective subproblems matches the state-of-the-art upper and lower complexity bound results on first-order projection free method. It also adds more features allowing for practical implementation. In the weakly smooth case when the gradient is Hölder continuous, both the gradient and linear objective complexity results of UCGS improve the current state-of-the-art upper complexity results. Within the class of sliding-type algorithms, to the best of our knowledge, this is the first time a sliding-type algorithm is able to improve not only the gradient complexity but also the overall complexity for computing an approximate solution.