Integer and combinatorial optimization
Integer and combinatorial optimization
A Polyhedral Study of the Cardinality Constrained Knapsack Problem
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
Models and Methods for Merge-in-Transit Operations
Transportation Science
Facets of the Complementarity Knapsack Polytope
Mathematics of Operations Research
Branch-and-cut for combinatorial optimization problems without auxiliary binary variables
The Knowledge Engineering Review
A family of inequalities for the generalized assignment polytope
Operations Research Letters
Models for representing piecewise linear cost functions
Operations Research Letters
Variable Disaggregation in Network Flow Problems with Piecewise Linear Costs
Operations Research
A family of inequalities valid for the robust single machine scheduling polyhedron
Computers and Operations Research
Modeling disjunctive constraints with a logarithmic number of binary variables and constraints
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
An approximation approach for representing S-shaped membership functions
IEEE Transactions on Fuzzy Systems
The hill detouring method for minimizing hinging hyperplanes functions
Computers and Operations Research
A special ordered set approach for optimizing a discontinuous separable piecewise linear function
Operations Research Letters
Nonconvex, lower semicontinuous piecewise linear optimization
Discrete Optimization
On linear programs with linear complementarity constraints
Journal of Global Optimization
Models and strategies for efficiently determining an optimal vertical alignment of roads
Computers and Operations Research
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We give a branch-and-cut algorithm for solving linear programs (LPs) with continuous separable piecewise-linear cost functions (PLFs). Models for PLFs use continuous variables in special-ordered sets of type 2 (SOS2). Traditionally, SOS2 constraints are enforced by introducing auxiliary binary variables and other linear constraints on them. Alternatively, we can enforce SOS2 constraints by branching on them, thus dispensing with auxiliary binary variables. We explore this approach further by studying the inequality description of the convex hull of the feasible set of LPs with PLFs in the space of the continuous variables, and using the new cuts in a branch-and-cut scheme without auxiliary binary variables. We give two families of valid inequalities. The first family is obtained by lifting the convexity constraints. The second family consists of lifted cover inequalities. Finally, we report computational results that demonstrate the effectiveness of our cuts, and that branch-and-cut without auxiliary binary variables is significantly more practical than the traditional mixed-integer programming approach.