{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:37:00Z","timestamp":1760060220396,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,8,7]],"date-time":"2025-08-07T00:00:00Z","timestamp":1754524800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Scientific Startup Foundation for Doctors of Northwest A&amp; F University","award":["Z1090324139","Z1090125002","RGPIN 2024-05941"],"award-info":[{"award-number":["Z1090324139","Z1090125002","RGPIN 2024-05941"]}]},{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["Z1090324139","Z1090125002","RGPIN 2024-05941"],"award-info":[{"award-number":["Z1090324139","Z1090125002","RGPIN 2024-05941"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]},{"name":"University of Alberta","award":["Z1090324139","Z1090125002","RGPIN 2024-05941"],"award-info":[{"award-number":["Z1090324139","Z1090125002","RGPIN 2024-05941"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>In this paper, we propose a sparse distributionally robust optimization (DRO) model incorporating the Conditional Value-at-Risk (CVaR) measure to control tail risks in uncertain environments. The model utilizes sparsity to reduce transaction costs and enhance operational efficiency. We reformulate the problem as a Min-Max-Min optimization and convert it into an equivalent non-smooth minimization problem. To address this computational challenge, we develop an approximate discretization (AD) scheme for the underlying continuous random vector and prove its convergence to the original non-smooth formulation under mild conditions. The resulting problem can be efficiently solved using a subgradient method. While our analysis focuses on CVaR penalty, this approach is applicable to a broader class of non-smooth convex regularizers. The experimental results on the portfolio selection problem confirm the effectiveness and scalability of the proposed AD algorithm.<\/jats:p>","DOI":"10.3390\/info16080676","type":"journal-article","created":{"date-parts":[[2025,8,8]],"date-time":"2025-08-08T09:56:42Z","timestamp":1754647002000},"page":"676","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["An Approximate Algorithm for Sparse Distributionally Robust Optimization"],"prefix":"10.3390","volume":"16","author":[{"given":"Ruyu","family":"Wang","sequence":"first","affiliation":[{"name":"College of Science, Northwest A&F University, Xianyang 712100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yaozhong","family":"Hu","sequence":"additional","affiliation":[{"name":"Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2G1, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cong","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Science, Northwest A&F University, Xianyang 712100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3557-893X","authenticated-orcid":false,"given":"Quanwei","family":"Gao","sequence":"additional","affiliation":[{"name":"College of Information Engineering, Northwest A&F University, Xianyang 712100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3190","DOI":"10.1016\/j.cma.2007.03.003","article-title":"Robust optimization\u2014A comprehensive survey","volume":"196","author":"Beyer","year":"2007","journal-title":"Comput. 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