Modelling piecewise linear concave costs in a tree partitioning problem
Discrete Applied Mathematics
Models and Methods for Merge-in-Transit Operations
Transportation Science
Exact solution of multicommodity network optimization problems with general step cost functions
Operations Research Letters
On the capacitated concentrator location problem: a reformulation by discretization
Computers and Operations Research
Variable Disaggregation in Network Flow Problems with Piecewise Linear Costs
Operations Research
0-1 reformulations of the multicommodity capacitated network design problem
Discrete Applied Mathematics
A Superior Representation Method for Piecewise Linear Functions
INFORMS Journal on Computing
Global optimization for first order Markov Random Fields with submodular priors
Discrete Applied Mathematics
On the capacitated concentrator location problem: a reformulation by discretization
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
Computers and Industrial Engineering
Inventory placement in acyclic supply chain networks
Operations Research Letters
A special ordered set approach for optimizing a discontinuous separable piecewise linear function
Operations Research Letters
Nonconvex, lower semicontinuous piecewise linear optimization
Discrete Optimization
Models for representing piecewise linear cost functions
Operations Research Letters
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We study a generic minimization problem with separable nonconvex piecewise linear costs, showing that the linear programming (LP) relaxation of three textbook mixed-integer programming formulations each approximates the cost function by its lower convex envelope. We also show a relationship between this result and classical Lagrangian duality theory.