{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,12,2]],"date-time":"2023-12-02T02:27:24Z","timestamp":1701484044219},"reference-count":22,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Asia Pac. J. Oper. Res."],"published-print":{"date-parts":[[2015,2]]},"abstract":"<jats:p> A quadratic optimization problem with one nonconvex quadratic constraint is studied using the canonical dual approach. Under the dual Slater's condition, we show that the canonical dual has a smooth concave objective function over a convex feasible domain, and this dual has a finite supremum unless the original quadratic optimization problem is infeasible. This supremum, when it exists, always equals to the minimum value of the primal problem. Moreover, a global minimizer of the primal problem can be provided by a dual-to-primal conversion plus a \"boundarification\" technique. Application to solving a quadratic programming problem over a ball is included and an error bound estimation is provided. <\/jats:p>","DOI":"10.1142\/s0217595915400072","type":"journal-article","created":{"date-parts":[[2015,2,12]],"date-time":"2015-02-12T03:43:19Z","timestamp":1423712599000},"page":"1540007","source":"Crossref","is-referenced-by-count":3,"title":["Canonical Dual Solutions to Quadratic Optimization over One Quadratic Constraint"],"prefix":"10.1142","volume":"32","author":[{"given":"Wenxun","family":"Xing","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, Tsinghua University, Beijing, China"}]},{"given":"Shu-Cherng","family":"Fang","sequence":"additional","affiliation":[{"name":"Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC, USA"}]},{"given":"Ruey-Lin","family":"Sheu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, National Cheng Kung University, Taiwan"}]},{"given":"Liping","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Tsinghua University, Beijing, China"}]}],"member":"219","published-online":{"date-parts":[[2015,2,11]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1137\/050644471"},{"key":"rf2","series-title":"MPS-SIAM Series on Optimization","volume-title":"Lectures on Modern Convex Optimization: Analysis, Algorithms, Engineering Applications","author":"Ben-Tal A.","year":"2000"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.3934\/jimo.2008.4.155"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/s10898-008-9378-7"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1080\/10556780410001647186"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1023\/A:1026537630859"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1023\/B:JOGO.0000048034.94449.e3"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-88619-0_3"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1007\/s10898-009-9399-x"},{"key":"rf10","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1090\/qam\/1012271","volume":"47","author":"Gao D. 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