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We start the discussion pointing out some weaknesses of the classical linear scalarization approach when applied to the considered class of problems. We are then motivated to propose a suitable algorithmic framework that is designed to overcome these limitations: the novel algorithm combines a gradient-based exploration-refinement strategy with a tailored initialization scheme based on memetic or multi-start descent procedures. Thorough computational experiments highlight how the proposed method is far superior to both linear scalarization and popular genetic algorithms.<\/jats:p>","DOI":"10.1007\/s10288-025-00600-3","type":"journal-article","created":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T17:48:39Z","timestamp":1757612919000},"page":"1-33","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the computation of the efficient frontier in advanced sparse portfolio optimization"],"prefix":"10.1007","volume":"24","author":[{"given":"Arturo","family":"Annunziata","sequence":"first","affiliation":[]},{"given":"Matteo","family":"Lapucci","sequence":"additional","affiliation":[]},{"given":"Pierluigi","family":"Mansueto","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4424-9185","authenticated-orcid":false,"given":"Davide","family":"Pucci","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,9,11]]},"reference":[{"issue":"1","key":"600_CR1","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1111\/j.1540-6261.1952.tb01525.x","volume":"7","author":"H Markowitz","year":"1952","unstructured":"Markowitz H (1952) Portfolio selection. 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