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Two different approximations of Peano-Hilbert curve applied to reduce the problem to a univariate one satisfying the H\u00f6lder condition are discussed. The first of them, piecewise-linear approximation, is broadly used in global optimization and not only whereas the second one, non-univalent approximation, is less known. Multi-dimensional geometric algorithms employing these Peano curve approximations are introduced and their convergence conditions are established. Numerical experiments executed on 800 randomly generated test functions taken from the literature show a promising performance of algorithms employing Peano curve approximations w.r.t. their direct competitors.\n<\/jats:p>","DOI":"10.1007\/s10898-022-01216-1","type":"journal-article","created":{"date-parts":[[2022,8,8]],"date-time":"2022-08-08T02:02:21Z","timestamp":1659924141000},"page":"707-722","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Numerical methods using two different approximations of space-filling curves for black-box global optimization"],"prefix":"10.1007","volume":"88","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1429-069X","authenticated-orcid":false,"given":"Yaroslav D.","family":"Sergeyev","sequence":"first","affiliation":[]},{"given":"Maria Chiara","family":"Nasso","sequence":"additional","affiliation":[]},{"given":"Daniela","family":"Lera","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,8,8]]},"reference":[{"key":"1216_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-68913-5","volume-title":"Derivative-Free and Blackbox Optimization","author":"C Audet","year":"2017","unstructured":"Audet, C., Hare, W.: Derivative-Free and Blackbox Optimization. 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