D-NMDT bilinear/quadratic approximation with optional T-D-NMDT tightening#41
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D-NMDT bilinear/quadratic approximation with optional T-D-NMDT tightening#41
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…A, remove dead code in epigraph.jl Co-authored-by: jd-lara <16385323+jd-lara@users.noreply.github.com>
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[WIP] Implement D-NMDT model with optional tightening
D-NMDT bilinear/quadratic approximation with optional T-D-NMDT tightening
Mar 10, 2026
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Implements D-NMDT and T-D-NMDT (Beach et al. 2024, Definitions 8–10) MIP relaxations for univariate squares x² and bilinear products x·y. Tightening via epigraph cuts is optional since the paper's results are inconclusive on performance.
Changes:
src/quadratic_approximations/dnmdt.jl— D-NMDT binary expansion, McCormick linearization, and optional T-D-NMDT epigraph tightening for both univariate and bivariate casestest/test_dnmdt_approximations.jl— Tests for binary expansion correctness, relaxation validity/gap bounds, tightening behavior, and D-NMDT vs HybS comparisonsrc/quadratic_approximations/epigraph.jl— Addedz_ubupper bound on epigraph variablesrc/quadratic_approximations/{bilinear,hybs,sawtooth}.jl— Added variable boundsBug fixes during merge with main:
HybSProductExpression→BilinearProductExpressionin testHYBS_METAfromtest_hybs_approximations.jlinclude order (now definesDNMDT_HYBS_METAlocally)step/breakpointsvariables inepigraph.jlleft over from pre-sawtooth implementation✨ Let Copilot coding agent set things up for you — coding agent works faster and does higher quality work when set up for your repo.