{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T17:04:31Z","timestamp":1773680671422,"version":"3.50.1"},"reference-count":14,"publisher":"American Mathematical Society (AMS)","issue":"248","license":[{"start":{"date-parts":[[2004,8,20]],"date-time":"2004-08-20T00:00:00Z","timestamp":1092960000000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>In this paper the Eigenvalue Complementarity Problem (EiCP) with real symmetric matrices is addressed. It is shown that the symmetric (EiCP) is equivalent to finding an equilibrium solution of a differentiable optimization problem in a compact set. A necessary and sufficient condition for solvability is obtained which, when verified, gives a convenient starting point for any gradient-ascent local optimization method to converge to a solution of the (EiCP). It is further shown that similar results apply to the Symmetric Generalized Eigenvalue Complementarity Problem (GEiCP). Computational tests show that these reformulations improve the speed and robustness of the solution methods.<\/p>","DOI":"10.1090\/s0025-5718-03-01614-4","type":"journal-article","created":{"date-parts":[[2004,6,11]],"date-time":"2004-06-11T19:05:00Z","timestamp":1086980700000},"page":"1849-1863","source":"Crossref","is-referenced-by-count":54,"title":["The symmetric eigenvalue complementarity problem"],"prefix":"10.1090","volume":"73","author":[{"given":"Marcelo","family":"Queiroz","sequence":"first","affiliation":[]},{"given":"Joaquim","family":"J\u00fadice","sequence":"additional","affiliation":[]},{"suffix":"Jr.","given":"Carlos","family":"Humes","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2003,8,20]]},"reference":[{"issue":"5","key":"1","doi-asserted-by":"publisher","first-page":"1186","DOI":"10.1137\/0520078","article-title":"Unconstrained variational principles for eigenvalues of real symmetric matrices","volume":"20","author":"Auchmuty, Giles","year":"1989","journal-title":"SIAM J. 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