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Prediction-correction alternating direction method for a class of constrained min-max problems. (English) Zbl 1201.65102

The authors consider a class of constrained min-max problems of the following form: \[ \min_{x\in X,z\in Z}\Biggl\{\max_{y\in Y}\,y^Tx\mid Ax+ Bz= b\Biggr\}. \] These problems can be solved by projection type prediction-correction methods. The authors use an alternating direction method to obtain components of the predictor one by one and prove the global convergence of the method.
Numerical results are given.

MSC:

65K05 Numerical mathematical programming methods
90C25 Convex programming
90C47 Minimax problems in mathematical programming
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