{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:30:42Z","timestamp":1787333442678,"version":"build-2736575974"},"reference-count":42,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Optim."],"published-print":{"date-parts":[[1998,2]]},"abstract":"<jats:p>In this paper we consider the problem of minimizing a (possibly nonconvex) quadratic function with a quadratic constraint. We point out some new properties of the problem. In particular, in the first part ofthe paper, we show that (i) given a KKT point that is not a global minimizer, it is easy to find a \"better\" feasible point; (ii) strict complementarity holds at the local-nonglobal minimizer. In the second part of this paper, we show that the original constrained problem is equivalent to the unconstrained minimization of a piecewise quartic merit function. Using the unconstrained formulation we give, in the nonconvex case, a new second order necessary condition for global minimizers. In the third part of this paper, algorithmic applications of the preceding results are briefly outlined and some preliminary numerical experiments are reported.<\/jats:p>","DOI":"10.1137\/s1052623494278049","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"105-122","source":"Crossref","is-referenced-by-count":36,"title":["On Some Properties of Quadratic Programs with a Convex Quadratic Constraint"],"prefix":"10.1137","volume":"8","author":[{"given":"Stefano","family":"Lucidi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Laura","family":"Palagi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Massimo","family":"Roma","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,31]]},"reference":[{"key":"R1","unstructured":"A. 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Mathematical Programming Society Conference on Integer Programming and Combinatorial Optimization, University of Waterloo, Waterloo, ON, Canada, 1990, pp. 351\u2013366.","DOI":"10.1090\/conm\/114\/1097880"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1007\/BF01582907"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1137\/0806017"},{"key":"R24","unstructured":"S. Lucidi and L. Palagi,\n                      A class of algorithms for large scale trust region problems\n                      , Tech. report 36.96, Dipartimento di Informatica e Sistemistica, Universit\u00e0 di Roma \u201cLa Sapienza,\u201d Roma, Italy, 1996."},{"key":"R25","unstructured":"S. Lucidi, L. Palagi, and M. Roma,\n                      Quadratic Programs with Quadratic Constraint: Characterization of KKT Points and Equivalence with an Unconstrained Problem\n                      , Tech. report 24.94, Dipartimento di Informatica e Sistemistica, Universit\u00e0 di Roma \u201cLa Sapienza,\u201d Roma, Italy, 1994."},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1137\/0804009"},{"key":"R27","doi-asserted-by":"publisher","DOI":"10.1007\/BF01585768"},{"key":"R28","doi-asserted-by":"publisher","DOI":"10.1080\/10556789308805542"},{"key":"R29","doi-asserted-by":"publisher","DOI":"10.1007\/BF01582091"},{"key":"R30","doi-asserted-by":"publisher","DOI":"10.1137\/0904038"},{"key":"R31","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(91)90267-Z"},{"key":"R32","unstructured":"M. Powell, A method for nonlinear constraints in minimization problems, Academic Press, London, 1969, 283\u201329842:7284"},{"key":"R33","unstructured":"F. Rendl and H. Wolkowicz,\n                      A Semidefinite Framework to Trust Region Subproblems with Applications to Large Scale Minimization\n                      , Tech. report CORR Rep. 94\u201032, University of Waterloo, Department of Combinatorics and Optimization, Waterloo, ON, Canada, 1994."},{"key":"R34","doi-asserted-by":"crossref","unstructured":"S. A. Santos and D. C. Sorensen,\n                      A New Matrix\u2010Free for the Large Scale Trust Region Subproblem\n                      , Tech. report TR95\u201020, Rice University, Houston, TX, 1995.","DOI":"10.21236\/ADA445632"},{"key":"R35","doi-asserted-by":"publisher","DOI":"10.1137\/0719026"},{"key":"R36","unstructured":"D. C. Sorensen,\n                      Minimization of a Large Scale Quadratic Function Subject to an Ellipsoidal Constraint\n                      , Tech. report TR94\u201027, Rice University, Houston, TX, 1994."},{"key":"R37","unstructured":"P. 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