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We also adapt the concept for sets and establish characterizations of the mentioned behavior in terms of the Bouligand tangent cones. The special case of convex functions and sets is also studied.<\/jats:p>","DOI":"10.1137\/080738271","type":"journal-article","created":{"date-parts":[[2010,2,5]],"date-time":"2010-02-05T18:13:37Z","timestamp":1265393617000},"page":"1766-1785","source":"Crossref","is-referenced-by-count":4,"title":["Various Lipschitz-like Properties for Functions and Sets I: Directional Derivative and Tangential Characterizations"],"prefix":"10.1137","volume":"20","author":[{"given":"Rafael","family":"Correa","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pedro","family":"Gajardo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lionel","family":"Thibault","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,2,5]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/S105262349732339X"},{"key":"R2","doi-asserted-by":"crossref","unstructured":"E. 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