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- W4287365087 abstract "This work develops a class of relaxations in between the big-M and convex hull formulations of disjunctions, drawing advantages from both. The proposed P-split formulations split convex additively separable constraints into P partitions and form the convex hull of the partitioned disjuncts. Parameter P represents the trade-off of model size vs. relaxation strength. We examine the novel formulations and prove that, under certain assumptions, the relaxations form a hierarchy starting from a big-M equivalent and converging to the convex hull. We computationally compare the proposed formulations to big-M and convex hull formulations on a test set including: K-means clustering, P_ball problems, and ReLU neural networks. The computational results show that the intermediate P-split formulations can form strong outer approximations of the convex hull with fewer variables and constraints than the extended convex hull formulations, giving significant computational advantages over both the big-M and convex hull." @default.
- W4287365087 created "2022-07-25" @default.
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- W4287365087 date "2021-01-29" @default.
- W4287365087 modified "2023-09-29" @default.
- W4287365087 title "Between steps: Intermediate relaxations between big-M and convex hull formulations" @default.
- W4287365087 doi "https://doi.org/10.48550/arxiv.2101.12708" @default.
- W4287365087 hasPublicationYear "2021" @default.
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