{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:23:46Z","timestamp":1787340226413,"version":"build-2736575974"},"reference-count":30,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"name":"Taiwan MOST","award":["109-2811-M-006-549"],"award-info":[{"award-number":["109-2811-M-006-549"]}]},{"DOI":"10.13039\/100020595","name":"National Science and Technology Council","doi-asserted-by":"publisher","award":["113-2115-M-006-012-MY2"],"award-info":[{"award-number":["113-2115-M-006-012-MY2"]}],"id":[{"id":"10.13039\/100020595","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12171021"],"award-info":[{"award-number":["12171021"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Optim."],"published-print":{"date-parts":[[2026,3,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>Given two [Formula: see text]-variate quadratic functions [Formula: see text] and [Formula: see text], we are interested in knowing whether or not the two hypersurfaces [Formula: see text] and [Formula: see text] intersect with each other. There are two ways of looking\u00a0at this problem. In one respect, the famous Finsler\u2013Calabi theorem (1936, 1964) asserts that if [Formula: see text] and [Formula: see text] are quadratic forms, [Formula: see text] and [Formula: see text] has no common solution other than the trivial one,\u00a0[Formula: see text], if and only if there exists a positive definite matrix pencil [Formula: see text]. The result is in general not true for nonhomogeneous quadratic functions. On the other hand, Levin (c.\u00a0late 1970s) tried to directly solve the intersection curve of [Formula: see text] and [Formula: see text] but it turned out to be way too ambitious. In this paper, we show that by incorporating the information about the unboundedness and the unattainability of several (at most 4) quadratic programming problems with one single quadratic constraint (QP1QC), the answer as to whether or not [Formula: see text] and [Formula: see text] intersect can be successfully determined.<\/jats:p>","DOI":"10.1137\/24m1674984","type":"journal-article","created":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T07:16:22Z","timestamp":1773040582000},"page":"381-408","source":"Crossref","is-referenced-by-count":0,"title":["A QP1QC Approach for Deciding Whether or Not Two Quadratic Surfaces Intersect"],"prefix":"10.1137","volume":"36","author":[{"given":"Huu-Quang","family":"Nguyen","sequence":"first","affiliation":[{"name":"Department of Mathematics, Vinh University, 43100 Nghe An, Vietnam."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ting-Tsen","family":"Lin","sequence":"additional","affiliation":[{"name":"Department of Industrial and Systems Engineering, University of Minnesota, Minneapolis, MN 55455 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ruey-Lin","family":"Sheu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, National Cheng Kung University, Tainan, Taiwan."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3522-7446","authenticated-orcid":true,"given":"Yong","family":"Xia","sequence":"additional","affiliation":[{"name":"LMIB of the Ministry of Education, School of Mathematical Sciences, Beihang University, Beijing, 100191 China."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2026,3,9]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-017-1206-8"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02573959"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1137\/15M1009871"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511804441"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1964-0166203-7"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1007\/0-387-29550-X_13"},{"key":"ref7","volume-title":"Solid Analytical Geometry and Determinants","author":"Dresden A.","year":"1964"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2007.10.006"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1145\/77055.77058"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1007\/BF01258188"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-2217(01)00143-6"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1007\/s00245-001-0034-6"},{"key":"ref13","first-page":"461","volume":"10","author":"Hsia Y.","year":"2014","journal-title":"Pac. 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