Random Sampling Many-Dimensional Sets Arising in Control

نویسندگان

چکیده

Various Monte Carlo techniques for random point generation over sets of interest are widely used in many areas computational mathematics, optimization, data processing, etc. Whereas regularly shaped such sampling is immediate to arrange, nontrivial, implicitly specified domains these not easy implement. We consider the so-called Hit-and-Run algorithm, a representative class Markov chain methods, which became popular recent years. To perform set, this method requires only knowledge intersection line through inside set with boundary set. This component procedure, known as oracle, has be performed quickly when applied economy representation many-dimensional within randomized approach mining, image reconstruction, control, In paper, we several vector and matrix typically encountered control by linear inequalities. Closed-form solutions proposed finding respective points intersection, leading efficient oracles; they generalized robust formulations where system matrices contain norm-bounded uncertainty.

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ژورنال

عنوان ژورنال: Mathematics

سال: 2021

ISSN: ['2227-7390']

DOI: https://doi.org/10.3390/math9050580