{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:34:19Z","timestamp":1787322859896,"version":"build-2736575974"},"reference-count":42,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2001,1]]},"abstract":"<jats:p>\n                    For P\n                    <jats:sub>0<\/jats:sub>\n                    -complementarity problems, most existing non--interior-point path-following methods require the existence of a strictly feasible point. (For a P\n                    <jats:sub>*<\/jats:sub>\n                    -complementarity problem, the existence of a strictly feasible point is equivalent to the nonemptyness and the boundedness of the solution set.) In this paper, we propose a new homotopy formulation for complementarity problems by which a new non--interior-point continuation trajectory is generated. The existence and the boundedness of this non--interior-point trajectory for P\n                    <jats:sub>0<\/jats:sub>\n                    -complementarity problems are proved under a very mild condition that is weaker than most conditions used in the literature. One prominent feature of this condition is that it may hold even when the often-assumed strict feasibility condition fails to hold. In particular, for a P\n                    <jats:sub>*<\/jats:sub>\n                    -problem it turns out that the new non--interior-point trajectory exists and is bounded if and only if the problem has a solution. We also study the convergence of this trajectory and characterize its limiting point as the parameter approaches zero.\n                  <\/jats:p>","DOI":"10.1137\/s0363012900372477","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"898-924","source":"Crossref","is-referenced-by-count":9,"title":["Existence and Limiting Behavior of a Non--Interior-Point Trajectory for Nonlinear Complementarity Problems Without Strict Feasibility Condition"],"prefix":"10.1137","volume":"40","author":[{"given":"Yun-Bin","family":"Zhao","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Duan","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,26]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1287\/moor.23.3.719"},{"key":"R2","doi-asserted-by":"crossref","unstructured":"JamesBurke, SongXu, A non\u2010interior predictor\u2010corrector path\u2010following method for LCP, Appl. Optim., Vol. 22, Kluwer Acad. Publ., Dordrecht, 1999, 45\u2013632000b:90091","DOI":"10.1007\/978-1-4757-6388-1_3"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1007\/s101079900111"},{"key":"R4","unstructured":"J. V. Burke and S. Xu,\n                      The Complexity of A Non\u2010Interior\u2010Path Following Method for the Linear Complementarity Problem\n                      , Technical report, Department of Mathematics, University of Washington, Seattle, WA, 1999."},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1137\/0614081"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623497321109"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1007\/PL00011375"},{"key":"R8","unstructured":"R. W. Cottle, J. S. Pang, and R. E. Stone,\n                      The Linear Complementarity Problem\n                      , Academic Press, Boston, 1992."},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(89)90463-1"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1287\/moor.23.3.735"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012997322935"},{"key":"R12","unstructured":"F. Facchinei and J. S. 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Xu,\n                      The Global Linear Convergence and Complexity of a Non\u2010Interior Path\u2010Following Algorithm for Monotone LCP Based on Chen\u2013Harker\u2013Kanzow\u2013Smale Smoothing Function\n                      , Technical report, Department of Mathematics, University of Washington, Seattle, WA, 1997."},{"key":"R36","doi-asserted-by":"publisher","DOI":"10.1007\/s101070050081"},{"key":"R37","doi-asserted-by":"publisher","DOI":"10.1109\/9.664151"},{"key":"R38","doi-asserted-by":"publisher","DOI":"10.1023\/A:1022606324827"},{"key":"R39","doi-asserted-by":"publisher","DOI":"10.1023\/A:1004674330768"},{"key":"R40","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012998345196"},{"key":"R41","doi-asserted-by":"publisher","DOI":"10.1023\/A:1026459501988"},{"key":"R42","doi-asserted-by":"publisher","DOI":"10.1287\/moor.26.1.119.10594"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0363012900372477","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:29:51Z","timestamp":1787318991000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0363012900372477"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,1]]},"references-count":42,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2001,1]]}},"alternative-id":["10.1137\/S0363012900372477"],"URL":"https:\/\/doi.org\/10.1137\/s0363012900372477","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001,1]]}}}