Disjunctive cuts in Mixed-Integer Conic Optimization
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10107_2022_1844_ReferencePDF.pdf
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Author(s)
Lodi, Andrea
Tanneau, Mathieu
Vielma, Juan-Pablo
Date Issued
June 27, 2022
Publisher
Springer Berlin Heidelberg
Citation
Lodi, Andrea, Tanneau, Mathieu and Vielma, Juan-Pablo. 2022. "Disjunctive cuts in Mixed-Integer Conic Optimization."
Version
Author's final manuscript
Abstract
Abstract
This paper studies disjunctive cutting planes in Mixed-Integer Conic Programming. Building on conic duality, we formulate a cut-generating conic program for separating disjunctive cuts, and investigate the impact of the normalization condition on its resolution. In particular, we show that a careful selection of normalization guarantees its solvability and conic strong duality. Then, we highlight the shortcomings of separating conic-infeasible points in an outer-approximation context, and propose conic extensions to the classical lifting and monoidal strengthening procedures. Finally, we assess the computational behavior of various normalization conditions in terms of gap closed, computing time and cut sparsity. In the process, we show that our approach is competitive with the internal lift-and-project cuts of a state-of-the-art solver.
MIT Department
Sloan School of Management
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s10107-022-01844-1
