Reverse propagation of McCormick relaxations
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Author(s)
Wechsung, Achim
Scott, Joseph K.
Barton, Paul I.
Watson, Harry Alexander James
Date Issued
April 2015
Journal
Journal of Global Optimization
Publisher
Springer US
Citation
Wechsung, Achim, Joseph K. Scott, Harry A. J. Watson, and Paul I. Barton. “Reverse Propagation of McCormick Relaxations.” J Glob Optim 63, no. 1 (April 23, 2015): 1–36.
Version
Author's final manuscript
Abstract
Constraint propagation techniques have heavily utilized interval arithmetic while the application of convex and concave relaxations has been mostly restricted to the domain of global optimization. Here, reverse McCormick propagation, a method to construct and improve McCormick relaxations using a directed acyclic graph representation of the constraints, is proposed. In particular, this allows the interpretation of constraints as implicitly defining set-valued mappings between variables, and allows the construction and improvement of relaxations of these mappings. Reverse McCormick propagation yields potentially tighter enclosures of the solutions of constraint satisfaction problems than reverse interval propagation. Ultimately, the relaxations of the objective of a non-convex program can be improved by incorporating information about the constraints.
MIT Department
Massachusetts Institute of Technology. Department of Chemical Engineering
Massachusetts Institute of Technology. Process Systems Engineering Laboratory
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/s10898-015-0303-6
