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- W2943555794 abstract "We consider dynamically generating linear constraints (cutting planes) to tighten relaxations for polynomial optimization problems. Many optimization problems have feasible set of the form $$S cap P$$ , where S is a closed set and P is a polyhedron. Integer programs are in this class and one can construct intersection cuts using convex “forbidden” regions, or S-free sets. Here, we observe that polynomial optimization problems can also be represented as a problem with linear objective function over such a feasible set, where S is the set of real, symmetric matrices representable as outer-products of the form $$xx^T$$ . Accordingly, we study outer-product-free sets and develop a thorough characterization of several (inclusion-wise) maximal intersection cut families. In addition, we present a cutting plane approach that guarantees polynomial-time separation of an extreme point in $$Psetminus S$$ using our outer-product-free sets. Computational experiments demonstrate the promise of our approach from the point of view of strength and speed." @default.
- W2943555794 created "2019-05-09" @default.
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- W2943555794 date "2019-01-01" @default.
- W2943555794 modified "2023-10-14" @default.
- W2943555794 title "Intersection Cuts for Polynomial Optimization" @default.
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- W2943555794 doi "https://doi.org/10.1007/978-3-030-17953-3_6" @default.
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