{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,9]],"date-time":"2026-07-09T08:19:08Z","timestamp":1783585148828,"version":"3.55.0"},"reference-count":42,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["12071234"],"award-info":[{"award-number":["12071234"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Tianjin universities","award":["TJYGZ43"],"award-info":[{"award-number":["TJYGZ43"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Asia Pac. J. Oper. Res."],"published-print":{"date-parts":[[2026,8]]},"abstract":"<jats:p>Markowitz [Portfolio selection. Journal of Finance, 7(1), 77\u201391] originates portfolio selection as the birth of modern finance. After his feat, Markowitz [Foundations of portfolio selection. Journal of Finance, 46(2),\u00a0469\u2013477] perceives general considerations in addition to variance and expected return of portfolio selection. However, there is relatively limited research in maximizing the considerations. In such an area, this paper theoretically enriches portfolio selection and makes contribution to the literature. Specifically, we obtain complete efficient sets\u2019 piecewise-linear-segment structure by parametric quadratic programming. Only by the structure, in theorems and corollaries, we prove the considerations as piecewise linear functions, maximize the considerations, and dominate stock-market indexes. Our models are general and universally fit numerous scenarios. Practically, we implement our models for the 30 component stocks of Dow Jones Industrial Average and 1937 US stocks of as a comprehensive sample, dominate the average, and can outperform the average out of sample.<\/jats:p>","DOI":"10.1142\/s0217595925500411","type":"journal-article","created":{"date-parts":[[2025,9,5]],"date-time":"2025-09-05T08:12:21Z","timestamp":1757059941000},"source":"Crossref","is-referenced-by-count":0,"title":["Post-Optimizing General Considerations for Portfolio Selection by Efficient Sets\u2019 Piecewise-Linear-Segment Structure via Parametric Quadratic Programming"],"prefix":"10.1142","volume":"43","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6486-0232","authenticated-orcid":false,"given":"Yue","family":"Qi","sequence":"first","affiliation":[{"name":"China Academy of Corporate Governance & Department of Financial Management, Business School, Nankai University, 94 Weijin Road, Tianjin 300071, P. R. 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