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On finding global optima for the hinge fitting problem

This paper considers the data fitting of n given points in by a hinge function, as it appears in Breiman (IEEE Trans. Inform. Theory 39(3) (1993) 999) and Pucar and Sjöberg (IEEE Trans. Inform. Theory 44(3) (1998) 1310). This problem can be seen as a mathematical programming problem with a convex objective function and equilibrium constraints. For the euclidean error, an enumerative approach is proposed, which...