Abstract
Usually, positively homogeneous functions are studied by means ofexhaustive families of upper and lower approximations and theirduals - upper and lower exhausters. Upper exhausters are used tofind minimizers while lower exhausters are employed to findmaximizers. In the paper, some properties of the so-calledconversion operator (which converts an upper exhauster into alower one, and vice versa) are discussed. The notions of cycle ofexhausters, minimal cycle of exhausters and equivalent exhaustersare introduced. A conjecture is formulated claiming that in thecase of polyhedral exhausters only 1-cycle minimal exhaustersexist.
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