Nonconvex minimax problems have attracted significant interest in machine learning and many other fields in recent years. In this paper, we propose a new zeroth-order alternatingrandomizedgradientprojection algorit...
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Nonconvex minimax problems have attracted significant interest in machine learning and many other fields in recent years. In this paper, we propose a new zeroth-order alternating randomized gradient projection algorithm to solve smooth nonconvex-linear problems and its iteration complexity to find an e-first-order Nash equilibrium is O(epsilon(-3)) and the number of function value estimation per iteration is bounded by O(d(x)epsilon(-2)). Furthermore, we propose a zeroth-order alternatingrandomized proximal gradientalgorithm for block-wise nonsmooth nonconvex-linear minimax problems and its corresponding iteration complexity is O(K-3/2 epsilon(-3)) and the number of function value estimation is bounded by O(d(x) epsilon(-2))per iteration. The numerical results indicate the efficiency of the proposed algorithms.
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