# Nonconvex-Nonconcave Min-Max Optimization with a Small Maximization Domain

@article{Ostrovskii2021NonconvexNonconcaveMO, title={Nonconvex-Nonconcave Min-Max Optimization with a Small Maximization Domain}, author={Dmitrii Ostrovskii and Babak Barazandeh and Meisam Razaviyayn}, journal={ArXiv}, year={2021}, volume={abs/2110.03950} }

We study the problem of finding approximate first-order stationary points in optimization problems of the form minx∈X maxy∈Y f(x, y), where the sets X,Y are convex and Y is compact. The objective function f is smooth, but assumed neither convex in x nor concave in y. Our approach relies upon replacing the function f(x, ⋅) with its k-th order Taylor approximation (in y) and finding a near-stationary point in the resulting surrogate problem. To guarantee its success, we establish the following…

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