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Exhausters, coexhausters and converters in nonsmooth analysis

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  • Usually, positively homogeneous functions are studied by means of exhaustive families of upper and lower approximations and their duals - upper and lower exhausters. Upper exhausters are used to find minimizers while lower exhausters are employed to find maximizers. In the paper, some properties of the so-called conversion operator (which converts an upper exhauster into a lower one, and vice versa) are discussed. The notions of cycle of exhausters, minimal cycle of exhausters and equivalent exhausters are introduced. A conjecture is formulated claiming that in the case of polyhedral exhausters only 1-cycle minimal exhausters exist.
    Mathematics Subject Classification: Primary: 90C30; Secondary: 65K05.


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