Learning and Propagating Lagrangian Variable Bounds for Mixed-Integer Nonlinear Programming

@inproceedings{Gleixner2013LearningAP,
  title={Learning and Propagating Lagrangian Variable Bounds for Mixed-Integer Nonlinear Programming},
  author={Ambros M. Gleixner and Stefan Weltge},
  booktitle={CPAIOR},
  year={2013}
}
Optimization-based bound tightening (OBBT) is a domain reduction technique commonly used in nonconvex mixed-integer nonlinear programming that solves a sequence of auxiliary linear programs. Each variable is minimized and maximized to obtain the tightest bounds valid for a global linear relaxation. This paper shows how the dual solutions of the auxiliary linear programs can be used to learn what we call Lagrangian variable bound constraints. These are linear inequalities that explain OBBT’s… CONTINUE READING
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