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A new concept is introduced: the quasi-descent direction. A point x is stationary on a set of search directions if there exists no feasible qdd on that set. The method does not require the computation of derivatives nor the explicit manipulation of asymptotically dense matrices. Preliminary numerical experiments carried out on small to medium problems are encouraging.<\/jats:p>","DOI":"10.1007\/s10589-023-00469-0","type":"journal-article","created":{"date-parts":[[2023,4,25]],"date-time":"2023-04-25T17:07:25Z","timestamp":1682442445000},"page":"821-856","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Convergence of derivative-free nonmonotone Direct Search Methods for unconstrained and box-constrained mixed-integer optimization"],"prefix":"10.1007","volume":"85","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0288-5522","authenticated-orcid":false,"given":"Ubaldo M.","family":"Garc\u00eda Palomares","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,4,25]]},"reference":[{"key":"469_CR1","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1007\/s11590-008-0089-2","volume":"3","author":"MA Abramson","year":"2009","unstructured":"Abramson, M.A., Audet, C., Chrissis, J.W., Walston, J.G.: Mesh adaptive direct search algorithms for mixed variable optimization. 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