Representability in mixed integer programming, I: characterization results
Discrete Applied Mathematics
Integer and combinatorial optimization
Integer and combinatorial optimization
Representation for multiple right-hand sides
Mathematical Programming: Series A and B
Disjunctive programming: properties of the convex hull of feasible points
Discrete Applied Mathematics
Polyhedral methods for piecewise-linear functions I: the lambda method
Discrete Applied Mathematics
Branch-and-cut for combinatorial optimization problems without auxiliary binary variables
The Knowledge Engineering Review
Nonconvex, lower semicontinuous piecewise linear optimization
Discrete Optimization
Approximating separable nonlinear functions via mixed zero-one programs
Operations Research Letters
Operations Research Letters
Models for representing piecewise linear cost functions
Operations Research Letters
Computing equilibria by incorporating qualitative models?
Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 1 - Volume 1
A Note on “A Superior Representation Method for Piecewise Linear Functions”
INFORMS Journal on Computing
Piecewise linear approximation of functions of two variables in MILP models
Operations Research Letters
Hi-index | 0.00 |
Many combinatorial constraints over continuous variables such as SOS1 and SOS2 constraints can be interpreted as disjunctive constraints that restrict the variables to lie in the union of m specially structured polyhedra. Known mixed integer binary formulations for these constraints have a number of binary variables and extra constraints that is linear in m. We give sufficient conditions for constructing formulations for these constraints with a number of binary variables and extra constraints that is logarithmic in m. Using these conditions we introduce the first mixed integer binary formulations for SOS1 and SOS2 constraints that use a number of binary variables and extra constraints that is logarithmic in the number of continuous variables. We also introduce the first mixed integer binary formulations for piecewise linear functions of one and two variables that use a number of binary variables and extra constraints that is logarithmic in the number of linear pieces of the functions. We prove that the new formulations for piecewise linear functions have favorable tightness properties and present computational results showing that they can significantly outperform other mixed integer binary formulations.