We give new facets and valid inequalities for the separable piecewise linear optimization knapsack polytope. We also extend the inequalities to the case in which some of the variables are semi-continuous. In a companion paper (de Farias, Gupta, Kozyreff, Zhao, 2011) we demonstrate the efficiency of the inequalities when used as cuts in a branch-and-cut … Read more
We report and analyze the results of our extensive computational testing of branch-and-cut for piecewise linear optimization using the cutting planes given recently by Zhao and de Farias. Besides analysis of the performance of the cuts, we also analyze the effect of formulation on the performance of branch-and-cut. Finally, we report and analyze initial results … Read more
Piecewise linear functions (PLFs) are commonly used to approximate nonlinear functions. They are also of interest in their own, arising for example in problems with economies of scale. Early approaches to piecewise linear optimization (PLO) assumed continuous PLFs. They include the incremental cost MIP model of Markowitz and Manne and the convex combination MIP model … Read more