Abstract: This paper proposes a block-alternating proximal gradient algorithm to solve block convex-nonconcave minimax optimization problems. The algorithm is a single loop algorithm. An each iteration of the algorithm, the proximal gradient method is used to alternately update each variable in the objective function. We have theoretically proved that the algorithm achieves an $\varepsilon$-stationary point in $\mathcal{O}\left( \varepsilon ^{-4} \right)$ iterations. To the best of our knowledge, this is the first time that a single loop algorithm has been proposed to solve a block convex-nonconcave minimax optimization problem.

Key words: minimax optimization problem, machine learning, alternating proximal gradient method