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. © 1999 Elsevier Science Ltd. All rights reserved.
Sun, X. L., & Li, D. (1999). Logarithmic-exponential penalty formulation for integer programming. Applied Mathematics Letters, 12(7), 73–77. https://doi.org/10.1016/S0893-9659(99)00104-4