Representability in mixed integer programming, I: characterization results
Discrete Applied Mathematics
Integer and combinatorial optimization
Integer and combinatorial optimization
Discrete Applied Mathematics
Polyhedral methods for piecewise-linear functions I: the lambda method
Discrete Applied Mathematics
Towards compatible triangulations
Theoretical Computer Science - Computing and combinatorics
Models and Methods for Merge-in-Transit Operations
Transportation Science
Variable Disaggregation in Network Flow Problems with Piecewise Linear Costs
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
Modeling disjunctive constraints with a logarithmic number of binary variables and constraints
Mathematical Programming: Series A and B
A special ordered set approach for optimizing a discontinuous separable piecewise linear function
Operations Research Letters
Nonconvex, lower semicontinuous piecewise linear optimization
Discrete Optimization
Parsimonious binary-encoding in integer programming
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
A Note on “A Superior Representation Method for Piecewise Linear Functions”
INFORMS Journal on Computing
The Nested Event Tree Model with Application to Combating Terrorism
INFORMS Journal on Computing
The hill detouring method for minimizing hinging hyperplanes functions
Computers and Operations Research
On linear programs with linear complementarity constraints
Journal of Global Optimization
Base-2 Expansions for Linearizing Products of Functions of Discrete Variables
Operations Research
Base-2 Expansions for Linearizing Products of Functions of Discrete Variables
Operations Research
INFORMS Journal on Computing
Improved integer programming approaches for chance-constrained stochastic programming
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Global optimization of bilinear programs with a multiparametric disaggregation technique
Journal of Global Optimization
Optimizing the implementation of real-time Simulink models onto distributed automotive architectures
Journal of Systems Architecture: the EUROMICRO Journal
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We study the modeling of nonconvex piecewise-linear functions as mixed-integer programming (MIP) problems. We review several new and existing MIP formulations for continuous piecewise-linear functions with special attention paid to multivariate nonseparable functions. We compare these formulations with respect to their theoretical properties and their relative computational performance. In addition, we study the extension of these formulations to lower semicontinuous piecewise-linear functions.