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We provide conditions under which the solution set of a nonsmooth and nonconvex optimization problem is non-empty and\/or compact. We also examine related properties such as the compactness of the sublevel sets, the boundedness from below and the coercivity of the objective function to characterize the non-emptiness and the compactness of the solution set of the underlying optimization problem under the unboundedness of its associated feasible set.\n<\/jats:p>","DOI":"10.1007\/s10957-025-02637-0","type":"journal-article","created":{"date-parts":[[2025,3,3]],"date-time":"2025-03-03T12:20:41Z","timestamp":1741004441000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Solution Existence and Compactness Analysis for Nonsmooth Optimization Problems"],"prefix":"10.1007","volume":"205","author":[{"given":"Nguyen Canh","family":"Hung","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0893-5604","authenticated-orcid":false,"given":"Thai Doan","family":"Chuong","sequence":"additional","affiliation":[]},{"given":"Nguyen Le Hoang","family":"Anh","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,3,3]]},"reference":[{"key":"2637_CR1","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1007\/s10107-019-01411-1","volume":"1","author":"AA Ahmadi","year":"2020","unstructured":"Ahmadi, A.A., Zhang, J.: On the complexity of testing attainment of the optimal value in nonlinear optimization. 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