Logarithmic-exponential penalty formulation for integer programming Original Research Article

The purpose of this note is to present a smooth penalty formulation for integer programming. By adopting the proposed logarithmic-exponential penalty function, we are able to transform an inequality constrained integer programming problem into an equivalent unconstrained problem with a smooth objective function when choosing an appropriate penalty parameter. We show that this penalty formulation preserves the convexity for convex integer programming problems.