Exactness Conditions for a Convex Differentiable Exterior Penalty for Linear Programming

Sufficient conditions are given for a classical dual exterior penalty function of a linear program to be independent of its penalty parameter. This ensures that an exact solution to the primal linear program can be obtained by minimizing the dual exterior penalty function. The sufficient conditions give a precise value to such a penalty parameter introduced in (Mangasarian, 2005), where no quantification of the parameter was given. Computational results on linear programs with up to one million variables or constraints compare favorably to CPLEX 9.0 (ILO, 2003) and validate the proposed approach.