In this paper, we develop two ``Nesterov's accelerated'' variants of the well-known extragradient method to approximate a solution of a co-hypomonotone inclusion constituted by the sum of two operators, where one is Lipschitz continuous and the other is possibly multivalued. The first scheme can be viewed as an accelerated variant of Tseng's forward-backward-forward splitting method, while the second one is a variant of the reflected forward-backward splitting method, which requires only one evaluation of the Lipschitz operator, and one resolvent of the multivalued operator. Under a proper choice of the algorithmic parameters and appropriate conditions on the co-hypomonotone parameter, we theoretically prove that both algorithms achieve $\mathcal{O}(1/k)$ convergence rates on the norm of the residual, where $k$ is the iteration counter. Our results can be viewed as alternatives of a recent class of Halpern-type schemes for root-finding problems.

翻译：在本文中,我们开发了两种“Nesterov”加速法的变体,即众所周知的超常法,以近似于解决由两个操作者加在一起构成的共聚苯丙诺酮的共聚物,其中一个操作者是Lipschitz连续的,另一个可能是多值的。第一个方案可以被视为Tseng前向后向前向前向分解法的加速变体,而第二个方案则是反映前向后向分解法的变体,它只需要对Lipschitz操作者和多值操作者进行一项评价,而另一个方案则需要多值的操作者。根据适当的算法参数和对共聚苯丙酮参数的适当条件选择,我们理论上证明两种算法在残余物的规范上都达到了$\mathcal{O}(1/k)合金的趋同率,而美元则是循环反。我们的结果可以被视为最近一类Halpern型的根调查问题的替代方案。