Geodesic
An extension of the Jacobi algorithm for the complementarity problem in the presence of multivalence
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 7, pp. 1167-1173

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The complementarity problem is examined in the case where the basic mapping is the sum of a finite number of superpositions of a univalent off-diagonal antitone mapping and a multivalent diagonal monotone one. An extension is proposed for the Jacobi algorithm, which constructs a sequence converging to a point solution. With the use of this property, the existence of a solution to the original problem is also established. Under certain additional conditions, the minimal element in the feasible set of this problem is one of its solutions. 
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     author = {I. V. Konnov},
     title = {An extension of the {Jacobi} algorithm for the complementarity problem in the presence of multivalence},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1167--1173},
     publisher = {mathdoc},
     volume = {45},
     number = {7},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_7_a2/}
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I. V. Konnov. An extension of the Jacobi algorithm for the complementarity problem in the presence of multivalence. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 7, pp. 1167-1173. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_7_a2/