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Publicação
Sharp Hybrid Zonotopes
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Orientador(es)
Resumo(s)
Mixed integer set representations, and specifically hybrid zonotopes, have enabled new techniques for reachability and verification of nonlinear and hybrid systems. Mixed-integer sets which have the property that their convex relaxation is equal to their convex hull are said to be sharp. This property allows the convex hull to be computed with minimal overhead, and is known to be important for improving the convergence rates of mixed-integer optimization algorithms that rely on convex relaxations. This letter examines methods for formulating sharp hybrid zonotopes and provides sharpness-preserving methods for performing several key set operations. This letter then shows how the reformulation-linearization technique can be applied to create a sharp realization of a hybrid zonotope that is initially not sharp. A numerical example applies this technique to find the convex hull of a level set of a feedforward ReLU neural network.
Descrição
Funding Information: This work was supported by the U.S. Department of Defense through the National Defense Science & Engineering Graduate (NDSEG) Fellowship Program. The work of Daniel Silvestre was supported by the FCT \u2013 Funda\u00E7\u00E3o para a Ci\u00EAncia e a Tecnologia through CTS - Centro de Tecnologia e Sistemas/UNINOVA/FCT/NOVA under Grant CTS/00066. Publisher Copyright: © IEEE. 2017 IEEE.
Palavras-chave
algebraic geometric methods Hybrid systems optimization Control and Systems Engineering Control and Optimization