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The convergence of PDM to a partial minimum of original problem is proved. Finally, numerical experiments using the S&amp;P index for 2020 are conducted to evaluate efficiency of the proposed algorithm in terms of return, variance and CVaR gaps and CPU times. <\/jats:p>","DOI":"10.1142\/s1793830923500210","type":"journal-article","created":{"date-parts":[[2023,3,5]],"date-time":"2023-03-05T04:38:25Z","timestamp":1677991105000},"source":"Crossref","is-referenced-by-count":2,"title":["A penalty decomposition algorithm for the extended mean\u2013variance\u2013CVaR portfolio optimization problem"],"prefix":"10.1142","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1950-8907","authenticated-orcid":false,"given":"Abdelouahed","family":"Hamdi","sequence":"first","affiliation":[{"name":"Program of Mathematics, Department of Mathematics, Statistics and Physics, College of Arts and Sciences, Qatar University, Doha, Qatar"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tahereh","family":"Khodamoradi","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maziar","family":"Salahi","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran"},{"name":"Center of Excellence for Mathematical Modeling, Optimization and Combinatorial Computing (MMOCC), University of Guilan, Rasht, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2023,4,4]]},"reference":[{"key":"S1793830923500210BIB001","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.1040.0201"},{"issue":"3","key":"S1793830923500210BIB002","first-page":"1","volume":"38","author":"Karbasy S. 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