On finding global optima for the hinge fitting problem

Authors:
M. Queiroz;C. Humes, Jr.;J. Júdice
Affiliations:
Computer Science Department, University of São Paulo, R. do Matão 1010, 05508-090 São Paulo, SP, Brazil;Computer Science Department, University of São Paulo, R. do Matão 1010, 05508-090 São Paulo, SP, Brazil;Mathematics Department, University of Coimbra, 3000 Coimbra, Portugal
Venue:
Computers and Operations Research
Year:
2004

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Abstract

This paper considers the data fitting of n given points in Rm 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 is a polynomial method in the sample size n, for a fixed dimension m. An alternative formulation for the l1 error is also introduced, which is processed by a Sequential Linear Complementarity Problem approach. Some numerical results with both algorithms are included to highlight the efficiency of those procedures.