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A primal-dual prediction-correction algorithm for saddle point optimization. (English) Zbl 1356.90160
Summary: In this paper, we introduce a new primal-dual prediction-correction algorithm for solving a saddle point optimization problem, which serves as a bridge between the algorithms proposed in [X. Cai et al., J. Glob. Optim. 57, No. 4, 1419–1428 (2013; Zbl 1282.90232)] and [B. He and X. Yuan, SIAM J. Imaging Sci. 5, No. 1, 119–149 (2012; Zbl 1250.90066)]. An interesting byproduct of the proposed method is that we obtain an easily implementable projection-based primal-dual algorithm, when the primal and dual variables belong to simple convex sets. Moreover, we establish the worst-case \(\mathcal O(1/t)\) convergence rate result in an ergodic sense, where \(t\) represents the number of iterations.

90C47 Minimax problems in mathematical programming
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