This paper presents smoothing schemes for obtaining approximate stationary
points of unconstrained or linearly-constrained composite nonconvex-concave
min-max (and hence nonsmooth) problems by applying well-known algorithms to
composite smooth approximations of the original problems. More specifically, in
the unconstrained (resp. constrained) case, approximate stationary points of
the original problem are obtained by applying, to its composite smooth
approximation, an accelerated inexact proximal point (resp. quadratic penalty)
method presented in a previous paper by the authors. Iteration complexity
bounds for both smoothing schemes are also established. Finally, numerical
results are given to demonstrate the efficiency of the unconstrained smoothing
scheme.

本文介绍了通过应用已知算法到原问题的复合平滑近似，获得无约束或线性约束的复合非凸凹、极小极大（因而是非光滑的）问题的近似稳定点的平滑方案。具体而言，在无约束（resp. 有约束）的情况下，通过应用作者先前提出的加速不精确近端点算法（resp. 二次罚项）到其复合平滑近似，获得原问题的近似稳态点。同时，还建立了两个平滑方案的迭代复杂度界。最后，给出了数值结果，以展示无约束平滑方案的效率。