The piecewise linear optimization polytope: new inequalities and intersection with semi-continuous constraints.

We give new facets and valid inequalities for the separable piecewise linear optimization (SPLO) knapsack polytope. We also extend the inequalities to the case in which some of the variables are semi-continuous. Finally, we give computational results that demonstrate their efficiency in solving difficult instances of SPLO and SPLO with semi-continuous constraints. [ABSTRACT FROM AUTHOR]