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A new derivative-free linesearch-based algorithmic framework is proposed to suitably handle those problems. First, a scheme for bound constrained problems that combines a dense sequence of directions to handle the nonsmoothness of the objective function with primitive directions to handle discrete variables is described. Then, an exact penalty approach is embedded in the scheme to suitably manage nonlinear (possibly nonsmooth) constraints. Global convergence properties of the proposed algorithms toward stationary points are analyzed and results of an extensive numerical experience on a set of mixed-integer test problems are reported.<\/jats:p>","DOI":"10.1007\/s10589-022-00363-1","type":"journal-article","created":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T19:03:46Z","timestamp":1648839826000},"page":"293-327","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Derivative-free methods for mixed-integer nonsmooth constrained optimization"],"prefix":"10.1007","volume":"82","author":[{"given":"Tommaso","family":"Giovannelli","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4063-8370","authenticated-orcid":false,"given":"Giampaolo","family":"Liuzzi","sequence":"additional","affiliation":[]},{"given":"Stefano","family":"Lucidi","sequence":"additional","affiliation":[]},{"given":"Francesco","family":"Rinaldi","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,4,1]]},"reference":[{"key":"363_CR1","first-page":"1","volume":"3","author":"M Abramson","year":"2004","unstructured":"Abramson, M., Audet, C.: Filter pattern search algorithms for mixed variable constrained optimization problems. 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