Valid inequalities for mixed 0-1 programs
Discrete Applied Mathematics
Integer and combinatorial optimization
Integer and combinatorial optimization
Strong formulations for mixed integer programming: a survey
Mathematical Programming: Series A and B
Modelling piecewise linear concave costs in a tree partitioning problem
Discrete Applied Mathematics
Valid inequalities and separation for capacitated fixed charge flow problems
Discrete Applied Mathematics
Exploring relaxation induced neighborhoods to improve MIP solutions
Mathematical Programming: Series A and B
A special ordered set approach for optimizing a discontinuous separable piecewise linear function
Operations Research Letters
Operations Research Letters
Models for representing piecewise linear cost functions
Operations Research Letters
Valid inequalities and separation for uncapacitated fixed charge networks
Operations Research Letters
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
On linear programs with linear complementarity constraints
Journal of Global Optimization
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A branch-and-cut algorithm for solving linear problems with continuous separable piecewise linear cost functions was developed in 2005 by Keha et al. This algorithm is based on valid inequalities for an SOS2 based formulation of the problem. In this paper we study the extension of the algorithm to the case where the cost function is only lower semicontinuous. We extend the SOS2 based formulation to the lower semicontinuous case and show how the inequalities introduced by Keha et al. can also be used for this new formulation. We also introduce a simple generalization of one of the inequalities introduced by Keha et al. Furthermore, we study the discontinuities caused by fixed charge jumps and introduce two new valid inequalities by extending classical results for fixed charge linear problems. Finally, we report computational results showing how the addition of the developed inequalities can significantly improve the performance of CPLEX when solving these kinds of problems.