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We provide new sufficient conditions for the outer-continuity, outer-openness and inner-openness of the solution mapping of (PSOP). By utilizing the property of cone-continuity, we derive sufficient conditions ensuring the Levitin-Polyak well-posedness for (PSOP) and the Hadamard well-posedness for a related parametric implicit set optimization problem (ISOP). Numerical examples are also given to illustrate the main results.<\/jats:p>","DOI":"10.1007\/s10957-025-02850-x","type":"journal-article","created":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T08:46:10Z","timestamp":1759135570000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Solution Stability and Well-Posedness for Classes of Parametric Set Optimization Problems"],"prefix":"10.1007","volume":"208","author":[{"given":"Zai-Yun","family":"Peng","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yue","family":"Zeng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0893-5604","authenticated-orcid":false,"given":"Thai Doan","family":"Chuong","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sangwoon","family":"Yun","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xin","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,9,29]]},"reference":[{"issue":"4","key":"2850_CR1","doi-asserted-by":"publisher","first-page":"1323","DOI":"10.1007\/s11117-021-00818-5","volume":"25","author":"LQ Anh","year":"2021","unstructured":"Anh, L.Q., Duy, T.Q., Khanh, P.Q.: Levitin-polyak well-posedness for equilibrium problems with the lexicographic order. 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