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- W3048395748 abstract "Abstract Valid linear inequalities are substantial in linear and convex mixed-integer programming. This article deals with the computation of valid linear inequalities for nonlinear programs. Given a point in the feasible set, we consider the task of computing a tight valid inequality. We reformulate this geometrically as the problem of finding a hyperplane which minimizes the distance to the given point. A characterization of the existence of optimal solutions is given. If the constraints are given by polynomial functions, we show that it is possible to approximate the minimal distance by solving a hierarchy of sum of squares programs. Furthermore, using a result from real algebraic geometry, we show that the hierarchy converges if the relaxed feasible set is bounded. We have implemented our approach, showing that our ideas work in practice." @default.
- W3048395748 created "2020-08-18" @default.
- W3048395748 creator A5073713999 @default.
- W3048395748 creator A5091353116 @default.
- W3048395748 date "2020-08-12" @default.
- W3048395748 modified "2023-10-16" @default.
- W3048395748 title "Generating Valid Linear Inequalities for Nonlinear Programs via Sums of Squares" @default.
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- W3048395748 doi "https://doi.org/10.1007/s10957-020-01736-4" @default.
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