Abstract
Sufficient conditions are given for a classical dual exterior penalty function of a linear program (LP) to be independent of its penalty parameter. This ensures that an exact solution to the primal LP can be obtained by minimizing the dual exterior penalty function. The sufficient conditions give a precise value to such a penalty parameter introduced in [O.L. Mangasarian, Exact 1-Norm support vector machines via unconstrained convex differentiable minimization, Tech. Rep. 05–03, Data Mining Institute, Computer Sciences Department, University of Wisconsin, Madison, Wisconsin, 2005. J. Machine Learn. Res. 7, 2006, pp. 1517–1530], where no quantification of the parameter was given. Computational results on LPs with up to one million variables or constraints compare favourably to ILOG CPLEX 9.0 users manual [ILOG CPLEX 9.0 User's Manual. ILOG, Incline Village, Nevada, 2003] and validate the proposed approach.
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