{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T11:32:21Z","timestamp":1772796741440,"version":"3.50.1"},"reference-count":41,"publisher":"Institute for Operations Research and the Management Sciences (INFORMS)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Management Science"],"published-print":{"date-parts":[[2026,3]]},"abstract":"<jats:p>Optimization problems with discrete decisions are nonconvex and thus lack strong duality, which limits the usefulness of tools such as shadow prices. It was shown in Burer (2009) that mixed-binary quadratic programs can be written as completely positive programs, which are convex. We apply this perspective by writing unit commitment in power systems as a completely positive program and then using the dual copositive program and strong duality to design new pricing mechanisms. We show that the mechanisms are revenue-adequate and, under certain conditions, support a market equilibrium. To facilitate implementation, we also employ a cutting plane algorithm for solving copositive programs exactly, which we further speed up via a second-order cone programming approximation. We provide numerical examples to illustrate the potential benefits of the pricing mechanisms and algorithms.<\/jats:p>\n                  <jats:p>This paper was accepted by Chung Piaw Teo, optimization.<\/jats:p>\n                  <jats:p>Supplemental Material: The online appendix and data files are available at https:\/\/doi.org\/10.1287\/mnsc.2023.00906 .<\/jats:p>","DOI":"10.1287\/mnsc.2023.00906","type":"journal-article","created":{"date-parts":[[2025,7,16]],"date-time":"2025-07-16T13:50:01Z","timestamp":1752673801000},"page":"2022-2040","source":"Crossref","is-referenced-by-count":0,"title":["Copositive Duality for Discrete Energy Markets"],"prefix":"10.1287","volume":"72","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4743-4776","authenticated-orcid":false,"given":"Cheng","family":"Guo","sequence":"first","affiliation":[{"name":"School of Mathematical and Statistical Sciences, Clemson University, Clemson, South Carolina 29634"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9276-3755","authenticated-orcid":false,"given":"Merve","family":"Bodur","sequence":"additional","affiliation":[{"name":"School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1304-9845","authenticated-orcid":false,"given":"Joshua A.","family":"Taylor","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, New Jersey Institute of Technology, Newark, New Jersey 07102"}]}],"member":"109","reference":[{"key":"B1","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2020.09.002"},{"issue":"2","key":"B2","first-page":"480","volume":"68","author":"Azizan N","year":"2020","journal-title":"Oper. 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