References

• E. Balas. Disjunctive programming: Properties of the convex hull of feasible points. Discrete Applied Mathematics 89(1–3):3–44, 1998. doi:10.1016/S0166-218X(98)00136-X. The formulation of a union of polyhedra used by ConvexPieces.
• C. D'Ambrosio, A. Lodi and S. Martello. Piecewise linear approximation of functions of two variables in MILP models. Operations Research Letters 38(1):39–46, 2010. doi:10.1016/j.orl.2009.09.005. Compares bivariate formulations with the separable reformulation.
• J. Huchette and J. P. Vielma. Nonconvex piecewise linear functions: Advanced formulations and simple modeling tools. Operations Research, 2023. doi:10.1287/opre.2019.1973, arXiv:1708.00050. The zig-zag and grid formulations (ZigZagBinary, ZigZagInteger, SixStencil, NineStencil, OptimalTriangleSelection, K1) and a computational comparison.
• J. Huchette and J. P. Vielma. A combinatorial approach for small and strong formulations of disjunctive constraints. Mathematics of Operations Research 44(3):793–820, 2019. arXiv:1607.04803. Independent branching formulations, including OptimalIndependentBranching.
• B. Lyu, I. V. Hicks and J. Huchette. Building formulations for piecewise linear relaxations of nonlinear functions. Operations Research, 2025. doi:10.1287/opre.2023.0187, arXiv:2304.14542. The Gray code and biclique cover formulations of IndependentBranching, and the formulation of piecewise linear relaxations with the binary variables of a single function, see UnivariatePWLRelaxation.
• J. P. Vielma. Embedding formulations and complexity for unions of polyhedra. Management Science 64(10):4721–4734, 2018. arXiv:1506.01417. The logarithmic embedding formulation LogarithmicEmbedding.
• J. P. Vielma, S. Ahmed and G. Nemhauser. Mixed-integer models for nonseparable piecewise-linear optimization: Unifying framework and extensions. Operations Research 58(2):303–315, 2010. The convex combination, multiple choice, disaggregated logarithmic and incremental formulations (ConvexCombination, MultipleChoice, DisaggregatedLogarithmic, Incremental).
• J. P. Vielma and G. Nemhauser. Modeling disjunctive constraints with a logarithmic number of binary variables and constraints. Mathematical Programming 128(1–2):49–72, 2011. The logarithmic independent branching formulation LogarithmicIndependentBranching and the UnionJack formulation.