Abstract
The aim of this paper is to establish a fundamental theory of convex analysis for the sets and functions over a discrete domain. By introducing conjugate/biconjugate functions and a discrete duality notion for the cones over discrete domains, we study duals of optimization problems whose decision parameters are integers. In particular, we construct duality theory for integer linear programming, provide a discrete version of Slater’s condition that implies the strong duality and discuss the relationship between integrality and discrete convexity.
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This work has been supported by US Army Research Office Grant (No. W911NF-15-1-0223) and The Scientific and Technological Research Council of Turkey Grant (No. 1059B191300653).
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Adıvar, M., Fang, SC. Convex Analysis and Duality over Discrete Domains. J. Oper. Res. Soc. China 6, 189–247 (2018). https://doi.org/10.1007/s40305-017-0158-2
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DOI: https://doi.org/10.1007/s40305-017-0158-2
Keywords
- Discrete convex analysis
- Discrete Lagrangian duality
- Discrete Slater’s condition
- Discrete strong duality
- Integer programming
- Integrality