{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T15:32:52Z","timestamp":1787239972598,"version":"build-2736575974"},"reference-count":39,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM Rev."],"published-print":{"date-parts":[[2004,1]]},"abstract":"<jats:p>We study stochastic linear-quadratic (LQ) optimal control problems over an infinite time horizon, allowing the cost matrices to be indefinite. We develop a systematic approach based on semidefinite programming (SDP). A central issue is the stability of the feedback control. We show that this can be effectively examined through the complementary duality of the SDP. Furthermore, we establish several implication relations among the SDP complementary duality, the (generalized) Riccati equation, and the optimality of the LQ control problem. Based on these relations, we propose a numerical procedure that provides a thorough treatment of the LQ control problem via primal-dual SDP: it identifies a stabilizing feedback control that is optimal or determines that the problem possesses no optimal solution. For the latter case, we develop an $\\epsilon$-approximation scheme that is asymptotically optimal.<\/jats:p>","DOI":"10.1137\/s0036144503434203","type":"journal-article","created":{"date-parts":[[2005,9,7]],"date-time":"2005-09-07T21:00:16Z","timestamp":1126126816000},"page":"87-111","source":"Crossref","is-referenced-by-count":9,"title":["Stochastic Linear-Quadratic Control via Primal-Dual Semidefinite Programming"],"prefix":"10.1137","volume":"46","author":[{"given":"David D.","family":"Yao","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shuzhong","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xun Yu","family":"Zhou","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,8,4]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1109\/9.863597"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/0117041"},{"key":"R3","unstructured":"F. 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Nemirovskii,\n                      Interior Point Polynomial Algorithms in Convex Programming\n                      , SIAM, Philadelphia, 1994."},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100030401"},{"key":"R24","unstructured":"J. F. 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Zhang, and X. Y. Zhou,\n                      Linear quadratic control revisited: A view through semidefinite programming\n                      . in Modeling, Control and Optimization of Complex Systems, W. Gong and L. Shi, eds., Kluwer Academic, Dordrecht, The Netherlands, 2002, Chapter 9, pp. 195\u2013235."},{"key":"R35","unstructured":"D. D. Yao, S. Zhang, and X. Y. Zhou,\n                      Tracking a Financial Benchmark Using a Few Assets\n                      , Technical Report SEEM2003\u201010, Department of Systems Engineering & Engineering Management, The Chinese University of Hong Kong, 2003;"},{"key":"R35","unstructured":"available online from http:\/\/www.se.cuhk.edu.hk\/\u223czhang\/Reports\/seem2003\u201010.ps."},{"key":"R36","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1466-3"},{"key":"R37","doi-asserted-by":"publisher","DOI":"10.1007\/s002450010003"}],"container-title":["SIAM Review"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0036144503434203","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T15:09:45Z","timestamp":1787238585000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0036144503434203"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,1]]},"references-count":39,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2004,1]]}},"alternative-id":["10.1137\/S0036144503434203"],"URL":"https:\/\/doi.org\/10.1137\/s0036144503434203","relation":{},"ISSN":["0036-1445","1095-7200"],"issn-type":[{"value":"0036-1445","type":"print"},{"value":"1095-7200","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,1]]}}}