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Based on this result, we develop several sufficient conditions to assure some desirable properties (nonemptyness, boundedness, and upper-semicontinuity) of a multivalued mapping associated with continuous (nonmonotone) complementarity problems corresponding to semimonotone, P$(\\tau, \\alpha, \\beta)$-, quasi-P\n                    <jats:sub>*<\/jats:sub>\n                    -, and exceptionally regular maps. The results proved in this paper generalize well-known results on the existence of central paths in continuous P\n                    <jats:sub>0<\/jats:sub>\n                    complementarity problems.\n                  <\/jats:p>","DOI":"10.1137\/s0363012998345196","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"571-593","source":"Crossref","is-referenced-by-count":17,"title":["Properties of a Multivalued Mapping Associated with Some Nonmonotone Complementarity Problems"],"prefix":"10.1137","volume":"39","author":[{"given":"Yun-Bin","family":"Zhao","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"George","family":"Isac","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":"publisher","DOI":"10.1007\/s101079900111"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623497321109"},{"key":"R4","unstructured":"B. Chen, X. Chen, and C. Kanzow,\n                      A Penalized Fischer\u2010Burmeister NCP\u2010Function: Theoretical Investigation and Numerical Results\n                      , Technical Report, Zur Angewandten Mathematik, Hamburger Beitr\u00e4ge, 1997."},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1137\/0614081"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623495280615"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1007\/BF00249052"},{"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","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144595285963"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008688302346"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1287\/moor.18.1.128"},{"key":"R15","unstructured":"O. 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Isac,\n                      Complementarity Problems\n                      , Lecture Notes in Math. 1528, Springer\u2010Verlag, Berlin, 1992.","DOI":"10.1007\/BFb0084653"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008284330108"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1023\/A:1021704311867"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479894273134"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1023\/A:1022659603268"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1007\/BF00932654"},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1007\/BF00940531"},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1287\/moor.16.4.754"},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-54509-3"},{"key":"R27","doi-asserted-by":"publisher","DOI":"10.1007\/BF01582283"},{"key":"R28","doi-asserted-by":"publisher","DOI":"10.1007\/BF01587074"},{"key":"R29","unstructured":"Zhi\u2010QuanLuo, PaulTseng, A new class of merit functions for the nonlinear complementarity problem, SIAM, Philadelphia, PA, 1997, 204\u201322598d:90125"},{"key":"R30","unstructured":"L.McLinden, The complementarity problem for maximal monotone multifunctions, Wiley, Chichester, 1980, 251\u201327081h:90137"},{"key":"R31","doi-asserted-by":"crossref","unstructured":"NimrodMegiddo, Pathways to the optimal set in linear programming, Springer, New York, 1989, 131\u201315890c:90147","DOI":"10.1007\/978-1-4613-9617-8_8"},{"key":"R32","doi-asserted-by":"publisher","DOI":"10.1007\/BF01587075"},{"key":"R33","doi-asserted-by":"publisher","DOI":"10.1287\/moor.21.3.629"},{"key":"R34","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719468"},{"key":"R35","unstructured":"G. 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Zhang,\n                      On Constructing Interior\u2010Point Path\u2010Following Methods for Certain Semimonotone Linear Complementarity Problems\n                      , Technical Report, Department of Computational and Applied Mathematics, Rice University, Houston, 1997."},{"key":"R43","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-6377(99)00024-3"},{"key":"R44","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008202323884"},{"key":"R45","doi-asserted-by":"publisher","DOI":"10.1023\/A:1021701913337"},{"key":"R46","doi-asserted-by":"publisher","DOI":"10.1023\/A:1004674330768"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0363012998345196","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T12:58:59Z","timestamp":1787230739000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0363012998345196"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,1]]},"references-count":46,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2000,1]]}},"alternative-id":["10.1137\/S0363012998345196"],"URL":"https:\/\/doi.org\/10.1137\/s0363012998345196","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,1]]}}}