We study constrained comonotone min-max optimization, a structured class of nonconvex-nonconcave min-max optimization problems, and their generalization to comonotone inclusion. In our first contribution, we extend the Extra Anchored Gradient (EAG) algorithm, originally proposed by Yoon and Ryu (2021) for unconstrained min-max optimization, to constrained comonotone min-max optimization and comonotone inclusion, achieving an optimal convergence rate of $O\left(\frac{1}{T}\right)$ among all first-order methods. Additionally, we prove that the algorithm's iterations converge to a point in the solution set. In our second contribution, we extend the Fast Extra Gradient (FEG) algorithm, as developed by Lee and Kim (2021), to constrained comonotone min-max optimization and comonotone inclusion, achieving the same $O\left(\frac{1}{T}\right)$ convergence rate. This rate is applicable to the broadest set of comonotone inclusion problems yet studied in the literature. Our analyses are based on simple potential function arguments, which might be useful for analyzing other accelerated algorithms.

翻译：我们研究受约束的共单调极小极大优化问题——这是非凸-非凹极小极大优化问题的一类结构化形式，及其向共单调包含问题的推广。首先，我们将Yoon和Ryu (2021) 针对无约束极小极大优化提出的额外锚定梯度(EAG)算法推广至受约束的共单调极小极大优化与共单调包含问题，在所有一阶方法中取得了最优收敛速率$O\left(\frac{1}{T}\right)$。此外，我们证明该算法的迭代过程收敛至解集中的一点。其次，我们将Lee和Kim (2021) 提出的快速额外梯度(FEG)算法推广至受约束的共单调极小极大优化与共单调包含问题，同样实现了$O\left(\frac{1}{T}\right)$的收敛速率。该速率适用于目前文献中研究的最广泛的一类共单调包含问题。我们的分析基于简洁的势函数论证方法，该方法可能对其他加速算法的分析具有参考价值。